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DO NOW! 1. Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t
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DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Dec 27, 2015

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Oswald Foster
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Page 1: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!1. Give the coordinates for the following points:

• A• B• C• D• E

2. Which line has the following equations:

• y=x• x=2• y=4

A

D

C

E

B

p

w

t

Page 2: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

AGENDA:• Do Now

• Transformations Intro

• Images and Pre-images• Isometries

• Translations!

• Definition• Rules

• Magnet Translations

• Exit Ticket and Packet Work Time

Page 3: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TRANSFORMATIONS!

TODAY, I WILL BE ABLE TO IDENTIFY ISOMETRIES AND FIND TRANSLATIONS OF IMAGES

Page 4: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

UNIT OBJECTIVE:BY THE END OF THIS UNIT SWBAT…Be as confident as Chris Brown when they look at ANY image and say …..

I CAN TRANSFORM YA!

Page 5: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

FIRST UP: DEFINING TRANSFORMATIONS!

A transformation is any change in the position, shape or size of a figure.

This includes when they move around, get bigger, get smaller, slide to the left, slide to the right, flip over... Basically anything you can do to a clip art on the computer is called a transformation.

Page 6: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

ESSSENTIAL WORDS TO KNOW:

Pre-Image: the original figure

Image: the resulting figure

Pre-Image

Image

This is always true!

Page 7: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

WORDS TO KNOW:

Isometry: a transformation in which the preimage and image are congruent

• Line segments are congruent when they have the same ____________?

• Angles are congruent when they have the same ___________?

So what do you think congruent shapes would look like?

Page 8: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

ARE THESE ISOMETRIES?

Page 9: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

ARE THESE ISOMETRIES?

Page 10: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAMING IMAGES

Described with between the pre-image and image.

A shape (like a line or a plane) is named by the points that make it up. For shapes these points are each at a vertex (where two lines meet).

The image of the shape can be named with prime notation (‘).

**The points have to stay in the same order between the pre-image and the image name.**

Page 11: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAME THAT TRANSFORMATION!

Page 12: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAME THAT TRANSFORMATION!

Page 13: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TRANSLATIONS

YOUR FIRST TYPE OF TRANSFORMATION!

THIS IS A SPECIFIC TYPE OF TRANSFORMATION!

Page 14: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TRANSLATION• A translation is a transformation that maps all

points of a figure the same distance and the same direction.

• A translation is ALWAYS an isometry!

• When you slide a figure in one direction it does not change the size, shape or orientation of the figure.

Page 15: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

HOW DO YOU KNOW HOW TO MOVE THE IMAGE?

• You know how to move a translation by looking at the rule. The rule is set up like an x and y coordinate: (x, y)

• Ex: (x+7, y-4) or (x-2, y+3)

• Each vertex on the pre-image is an x and y coordinate. You must apply the same rule to each point on the pre-image in order for it to be a translation.

Page 16: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

HOW DO YOU KNOW HOW TO MOVE THE IMAGE?

The first part of each rule tells you to move left or right.

• Negative numbers = move to the left

• Positive numbers = move to the right

EX:

• Rule: (x+4, y-5)

• Move each point on the pre-image to the right 4 units• Rule: (x-2, y+3)

• Move each point on the pre-image to the left 2 units

Page 17: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

HOW DO YOU KNOW HOW TO MOVE THE IMAGE?

The second half of each rule tells you to move up or down.

• Negative numbers = moving down

• Positive numbers = moving up

EX:

• Rule: (x+4, y-5)

• Move each point on the pre-image down 5 units• Rule: (x-2, y+3)

• Move each point on the pre-image up 3 units

Page 18: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

HOW DO YOU KNOW HOW TO MOVE THE IMAGE?

• Apply BOTH parts of the rule to every single vertex in the figure.

• Every point will move left or right and up or down the exact same amount.

• (x-2, y+5)

• Be sure to label every new point as a translated point.

Page 19: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

SHOW ME THE IMAGE!

, 1, 4x y x y

Page 20: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

GIVE ME THE NEW COORDINATES!

, 3, 3x y x y

Page 21: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

HOW DO YOU SAY HOW YOU MOVED THE IMAGE?• Rules for transformations are written as adapted (x,y) coordinate points.

• You simply count how much you’ve moved left or right. That is what you put with the x.

• Movement to the left is a negative move.• Movement to the right is a positive move.

• Then you count how much you’ve moved up or down. That is what you put with the y.

• Movement down is a negative move.• Movement up is a positive move.

Page 22: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

BUILDING THE RULE!

Page 23: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TELL ME THE RULE!

Page 24: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

LET’S PRACTICE!

Fill in the answers to these problems in the boxes on your classwork sheet for today. This will get you credit for today.

You can work with the people around you but you must remain in your seat as we work through these examples.

If you finish and problems early simply work on your IP #1 on Page 2 and 3. Be sure to check your answers with our work as we go along though!

Page 25: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

GIVE ME MY NEW COORDINATES!• In moving :

• A with the rule (x-3, y+4)

• F with the rule (x+4, y+9)

• G with the rule (x-1, y+7)

• C with the rule (x-3, y-5)

Page 26: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

WHAT IS THE RULE?• That moves:

• A to B

• C to F

• H to A

• G to B

Page 27: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TELL ME THE RULE!

Page 28: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

GIVE THE NEW COORDINATES!

What are the coordinates of triangle GHF after a translation with the rule (x-2, y+5)?

Page 29: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

EXIT TICKET

When you finish turn this into the tray and work on your IP on Page 2 and 3 in your notes packet!

1) Write the rule for the translation to the left.

2) Is this an isometry? How do you know?

Page 30: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!What are the equations of the following lines:

1. p

2. t

3. w

4. r

5. f

Remember that “x=“ lines will intersect the x-axis and “y=“ lines intersect the y-axis.

p

w

tf

r

Page 31: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

AGENDA:• Do Now

• Translations Quick Check

• Reflections!

• Introduction• Examples

• Reflections Buddies

• Packet Practice Time

Page 32: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

EXIT TICKET

Do this on a scrap sheet of paper. When you finish turn this into the tray and work on your IP on Page 2 and 3 in your notes packet!

1) Write the rule for the translation to the left.

2) Is this an isometry? How do you know?

Page 33: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTIONS!

TODAY I WILL BE ABLE TO…

FIND REFLECTION IMAGES OF FIGURES

THIS IS YOUR 2ND TYPE OF TRANSFORMATION!

Page 34: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

WHAT’S A REFLECTION?

A reflection is a flip of an object over a line. (like you are looking in a mirror)

Each point of the original figure (also called the what?) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line.

Under a reflection, the size of the figure does not change.

SO are reflections isometries or not?

Page 35: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAMED LIKE ANY TRANSFORMATION

Points have new letters or are named with the ‘ symbol, which is read _______________.

All points must remain in the same order as the preimage name no matter how you name them originally.

Page 36: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAMED LIKE ANY TRANSFORMATION

If We Perform a Reflection, A becomes _____, B becomes _____, C becomes _____ & so on.

So in this example….

Page 37: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS THE X-AXIS

A=

B=

C=

D=

A’=

B’=

C’=

D’=

A

C

B

D

Page 38: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS THE X-AXIS

A=

B=

C=

A’=

B’=

C’=

A

C

B

Page 39: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS THE Y-AXIS

A=

B=

C=

D=

A’=

B’=

C’=

D’=

A

C

B

D

Page 40: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS THE Y-AXIS

A=

B=

C=

A’=

B’=

C’=

A

C

B

Page 41: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS A GIVEN LINE

A=

B=

C=

D=

A’=

B’=

C’=

D’=

A

C

B

D

x= -1

Page 42: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS A GIVEN LINE

A=

B=

C=

D=

A’=

B’=

C’=

D’=

A

C

B

D

y= -1

Page 43: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTION ACROSS A GIVEN LINE

A=

B=

C=

A’=

B’=

C’=

A

C

B

y= x

Page 44: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

LET’S TRY IT!

1) What are the coordinates of H reflected across the y-axis?

Page 45: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

LET’S TRY IT!

2) What are the coordinates of H reflected across the x-axis?

Page 46: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

LET’S TRY IT!

3) What are the coordinates of G reflected across the line x=3?

Page 47: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

LET’S TRY IT!

4) Graph FGH and its reflection image across the line y = 4.

Page 48: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

LET’S TRY IT!

5) Graph FGH and its reflection image across the line y = -1.

Page 49: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

REFLECTIONS BUDDIES• Each of you will be given a card with one half of a famous couple (Ex:

Jennifer Lopez would have, up until recently, gone with- Marc Anthony)

• Your first task is to find your partner

• One of you will have a set of coordinates on your card. These will be the coordinates of your pre-image. You can fill these in on your classwork sheet.

• You must find these coordinates on the floor grid. The two axis's are marked and each square tile on the floor counts as one unit on the grid.

• Then you must use that original pre-image to find the coordinates of that point if it reflected across different lines.

• You will record all of these coordinates on your classwork sheet for today. Be sure to use the coordinates given on your card as the pre-image for each reflection.

• You can use the floor grid to help find your reflections.

• Let’s try an example:

• Pretend I have _____ on my card, so I need to find my partner ______.• My partner has the coordinates (3,2) on their card. I record that.• Now we need to reflect it over the: x-axis, y-axis…

Page 50: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

EXIT TICKETWrite it on the same piece of paper as yesterday. I will be handing them back to you.

2)

Page 51: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TONIGHT’S PRACTICE:

For tonight:

•Page 2 and 3 and Page 5 and 6 in your Unit 3 Notes Packet

Be sure you have these pages done tomorrow.

Page 52: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!What are the equations of the following lines:

1. p

2. t

3. w

4. r

5. f

Have your homework on the edge of your desk for me to check!

p

w

t

f

r

Page 53: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!

What are the coordinates of triangle GFH when it is reflected across the x-axis?

If you get stuck check your notes from yesterday or ask your neighbor!

Page 54: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

AGENDA:

• Do Now

• Homework Check

• Dilations!

• Project Introduction

• Packet Practice Time

Page 55: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

HOMEWORK CHECK:Unless you are writing a number on the board there is no reason to be out of your seat for any reason during this time.

First 5 minutes: Work with people around you and pick one question you really struggled with. Write the page number and problem number on the board.

Next 5 minutes: I will go over trouble problems for as long as you are silent. You talk, I stop. It’s that simple.

Page 56: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DILATIONS!

YOUR THIRD TYPE OF TRANSFORMATION!

TODAY I WILL BE ABLE TO…

DILATE IMAGES WHEN GIVEN A SCALE FACTOR

Page 57: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Reflections, rotations, and transformations all change the location of a point or figure

Dilations are different, they change the SIZE of the figure, either making it LARGER or smaller.

Scale factor: tells us how much larger or smaller the figure will become

Figure A

Figure A’

Figure A’

Page 58: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

When you dilate a shape, you change its size

How?

Multiply each vertex in the preimage by the scale factor.

• Enlargement: when the shape gets bigger

• A scale factor larger than 1

• Reduction: when the shape gets smaller• A scale factor smaller than 1

Page 59: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

When you dilate a shape, you change its sizeHow?

Example: Enlarge triangle YNI by a factor of 2 from the projection point j

j

y

n

i

Y’

N’

I’

The distance from the dilation point to each vertex increases (multiplies) by the factor indicated

Page 60: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Example: Enlarge the quadrilateral by a

factor of 3 from the projection point p

p

Page 61: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Dilate the triangle by a scale factor of ½ from the

projection point p

p

Page 62: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Now, try some dilations on a coordinate plane!

You can still draw lines from the dilation point to each

vertex…

Enlarge the triangle by a factor of 2 from a center of dilation (projection

point) at the origin.

Page 63: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

You can still draw lines from the dilation point to each

vertex…

ORyou can count boxes!

Enlarge the triangle by a factor of 2 from a center of dilation (projection

point) at the origin.

Page 64: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MA

T H

BC

A

w x

z y

w x

z yBC

A

U

LV

Enlarge the figure by a scale

factor of 2 from the center of dilation at point z.

Enlarge the figure by a scale

factor of 2 from the center of dilation at the origin.

Draw the dilated image of triangle ABC with a center of

dilation at the origin and a scale factor of ½

Draw the dilated image of triangle ABC with a center of dilation at

vertex A and a scale factor of ½

Enlarge trapezoid MATH by a factor of 3 around the center of the figure.

Enlarge LUV by a factor of 1.5 around point (0,-1).

Page 65: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

w x

z y

Enlarge the figure by a scale factor of 2 from the center of dilation

at point z.

w’ x’

z’ y’

The distance from the center of dilation (z) to each vertex has

been doubled (multiplied times 2)

Page 66: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

w x

z y

Dilate the figure by a scale factor of 2 from the center of dilation

at the origin.w’ x’

z’ y’

The distance from the center to each vertex

has been doubled (multiplied times 2)

Page 67: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

w x

z y

Notice: Each image is a result of a dilation by a factor of 2 so they are the same size.

Length was 33 x 2 = 6Length is now 6

Width was 22 x 2 = 4Width is now 4

Page 68: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

A

BC

A’

B’C’

Draw the dilated image of triangle ABC with the center of dilation at the

origin and a scale factor of ½

If you dilate by a factor less than 1, does your shape get

larger or smaller?

SMALLER

Page 69: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

A

BC

Draw the dilated image of triangle ABC with the

center of dilation at vertex A and a scale

factor of ½

A’

B’C’Which vertex did

not change after the dilation?

A and A’ are both at (0,4)

Page 70: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

A

BC

Notice: Each image is a result of a dilation by a factor of ½ so they are the same size.

Page 71: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MA

T H

M’A’

T’ H’

Dilate trapezoid MATH by a factor of 3 around the center

of the figure.

So the height of the figure was 2 units,

what is it now?

6 units

Page 72: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

U

LV

Enlarge LUV by a factor of 1.5 around

the point (0,-1)

L’V’

U’

Where is the center of dilation?

(0,-1)

Page 73: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

U

LV

Enlarge LUV by a factor of 2 around

the origin

Page 74: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

YOUR TURN TO TRY!

Take the next ten minutes to try a few practice problems on your own.

You will be working on Page 12 and 13. Try number 5-17 first.

If you finish early you can work on Page 5 and 6, which will be your homework tonight.

Please be sitting in your seat and working for the entire time. I will be coming around to help when you’re stuck, but please help each other if I am busy. There is no reason to be sitting and not working.

Page 75: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

PROJECT TIME!These will be worth a full quiz grade.

The project will be due on Monday and you will have class time tomorrow to work on it.

The whole project can be done in class if you use time wisely!

It is essential that you follow all directions and finish every part of the project if you want full credit.

Be sure that the original shape you create can be transformed in all the different ways we have been practicing. If your shape is too complicated you might not be able to transform it.

You use the original points every time you transform!

Feel free to use color and make it beautiful so I can hang it up when you are finished.

If there are any references to sex, drugs, alcohol, gangs or curse words you will automatically get a zero for the entire project.

Page 76: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TONIGHT’S PRACTICE:

For tonight:

•Page 5 and 6 in your Unit 3 Notes Packet

Be sure you have these pages done tomorrow.

Page 77: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW:• Get with your group and prepare for your presentation. You will

have 15 minutes to prep as long as I see everyone is working.

• Remember when you present you must turn in:

• Your posters• Your written out math work

• Each person must:

• Look appropriate• Be prepared to speak

Your entire presentation must:

• Take 4-5 minutes• Cover every answer• Reference your posters

Page 78: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

PRESENTATION TIME!

You must be silent while other groups present.

If I have to talk to you about speaking during presentations you will lose a point off your final grade.

Each presentation:

• Must be 4-5 minutes

• Must include references to your poster

• Must have each group member speak

• Have work to turn in with it.

Page 79: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!

• What are the coordinates of triangle HFG when it is reflected across the line x= 1?

• What are the coordinates of triangle HFG when it is dilated by a scale factor of ½ around the origin?

Page 80: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

WHAT ARE WE UP TO TODAY?

• Do Now

• Project Turn-In

• Board Races Quick Review

• Notes: Rotations

• Gallery Walk

• Packet Practice

Page 81: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

ROTATIONS!

THE 4TH TYPE OF TRANSFORMATION WE HAVE LEARNED!

TIWBAT…

ROTATE AN IMAGE ON A COORDINATE PLANE

Page 82: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

WHAT’S A ROTATION?

A rotation is a transformation that turns a figure around a point

The point around which an object spins is called the center of rotation.

A rotation of __________ degrees places an object back at its original location.

That is how many degrees are in a full circle! So it just ends up where it started!

Page 83: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DIRECTION OF ROTATIONS!

When not specified, an object is rotating ________________!

If a full circle is 360 degrees, then each quadrant of a circle is _______ degrees.

counterclockwise

90

Page 84: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

YOU CAN ALREADY SOLVE ROTATIONS WORD PROBLEMS.

JUST THINK IT THROUGH AND TRY IT OUT!

Page 85: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

#1 – A MERRY-GO-ROUND HAS 12 HORSES, EVENLY SPACED AROUND THE OUTSIDE. IF THE RIDE STARTS ENOUGH THAT THE FIRST HORSE IS NOW IN THE SECOND HORSE’S POSITION, HOW FAR HAS THE HORSE ROTATED?

Page 86: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

#2 – YOU WATCH THE CLOCK FROM 3:05 TO 3:25. HOW MANY DEGREES HAS THE MINUTE HAND ROTATED AND IN WHAT DIRECTION?

Page 87: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.
Page 88: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

THE RULES OF ROTATIONS:

COUNTERCLOCKWISE Rotation

Original Coordinate New Coordinate

90˚ (x,y) (-y,x)

180˚ (x,y) (-x,-y)

270˚ (x,y) (y,-x)

360˚ (x,y) (x,y)

Page 89: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.
Page 90: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.
Page 91: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.
Page 92: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

EX 1: ROTATE TRIANGLE ABC

A=

B=

C=

A’=

B’=

C’=

Page 93: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

EX 2: ROTATE JKLM

J=

K=

L=

M=

J’=

K’=

L’=

M’=

Page 94: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAME THAT ROTATION

Page 95: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NAME THAT ROTATION

Page 96: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

EXIT TICKETWhat type of rotation took you from Figure 1 to Figure 2?

(I need to know direction and degree)

If you can do this you got it!

Page 97: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

PARTNER GALLERY WALK• You are going to get a notecard with one half of a famous couple. You

must find your buddy first. This is your partner for the gallery walk.

• Now I want you to each take a marker and find your own station.

• At each station you go to today you will first makr your original point (which has its coordinates on the back of one of your cards) and name it. Do that now!

• Then you will read and follow the instructions for your given point at that specific station.

• Be sure you get your preimage and image point at every station. You will have one minute at each station and then you will ROTATE to the next station.

• Bring your packet with you and work on pages 8-10 in your packet if you finish any station early.

Page 98: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TONIGHT’S PRACTICE:

For tonight:

•Page 8-10 in your Unit 3 Notes Packet

Be sure you have these pages done tomorrow so you don’t get behind. Remember your entire packet is due during the test on Friday!

Page 99: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MIDTERM REMINDERS:• THERE IS ABSOLUTELY NO TALKING!!

• If you talk you will get an automatic zero and will be forced to come in and take your exam at another time or you will be failing this class.

• There are no re-takes or corrections for this exam so please do your best today.

• Each multiple choice question is worth 2 points. Correct answers are worth 2 points. If you get a wrong answer and have shown work in the corresponding box you will be able to make up 1 point.

• There are two calculators up front. Only one person may be at the calculator at a time.

• When you finish please bring your exam to me and then work on test corrections, missing work, write me a poem, draw me a picture or just put your head down and take a nap. The one thing you cannot do is talk at all.

Page 100: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!

1) What are the coordinates of triangle HGF when it is rotated 180 degrees clockwise around the origin?

Hint: Check the rule for 180 degree rotations in your rotations notes!

Page 101: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

AGENDA:• Do Now

• Rotations Quick Review• Dilations Notes

• Examples• Partner Work

• Test corrections and make-up work

• Work on test corrections• Be prepared for re-tests• Massive paper handback

Page 102: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DILATIONS!

YOUR FOURTH AND FINAL TYPE OF TRANSFORMATION!

Page 103: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Reflections, rotations, and transformations all change the location of a point or figure

Dilations are different, they change the SIZE of the figure, either making it LARGER or smaller.

Scale factor: tells us how much larger or smaller the figure will become

Figure A

Figure A’

Figure A’

Page 104: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

When you dilate a shape, you change its size

How?

Multiply each vertex in the preimage by the scale factor.

• Enlargement: when the shape gets bigger

• A scale factor larger than 1

• Reduction: when the shape gets smaller• A scale factor smaller than 1

Page 105: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

When you dilate a shape, you change its sizeHow?

Example: Enlarge triangle YNI by a factor of 2 from the projection point j

j

y

n

i

Y’

N’

I’

The distance from the dilation point to each vertex increases (multiplies) by the factor indicated

Page 106: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Example: Enlarge the quadrilateral by a

factor of 3 from the projection point p

p

Page 107: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Dilate the triangle by a scale factor of ½ from the

projection point p

p

Page 108: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

Now, try some dilations on a coordinate plane!

You can still draw lines from the dilation point to each

vertex…

Enlarge the triangle by a factor of 2 from a center of dilation (projection

point) at the origin.

Page 109: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

You can still draw lines from the dilation point to each

vertex…

ORyou can count boxes!

Enlarge the triangle by a factor of 2 from a center of dilation (projection

point) at the origin.

Page 110: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MA

T H

BC

A

w x

z y

w x

z yBC

A

U

LV

Enlarge the figure by a scale

factor of 2 from the center of dilation at point z.

Enlarge the figure by a scale

factor of 2 from the center of dilation at the origin.

Draw the dilated image of triangle ABC with a center of

dilation at the origin and a scale factor of ½

Draw the dilated image of triangle ABC with a center of dilation at

vertex A and a scale factor of ½

Enlarge trapezoid MATH by a factor of 3 around the center of the figure.

Enlarge LUV by a factor of 1.5 around point (0,-1).

Page 111: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

w x

z y

Enlarge the figure by a scale factor of 2 from the center of dilation

at point z.

w’ x’

z’ y’

The distance from the center of dilation (z) to each vertex has

been doubled (multiplied times 2)

Page 112: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW!

1) What are the coordinates of triangle HGF when it is rotated 90 degrees clockwise around the origin?

Hint: Check the rule for 90 degree rotations in your rotations notes!

Page 113: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

AGENDA:• Do Now

• Rotations Quick Review• Dilations Notes

• Examples• Progress Reports

• Test corrections and make-up work

• Work on test corrections• Make up all missing work• Be prepared for all re-tests for tomorrow

Page 114: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

w x

z y

Dilate the figure by a scale factor of 2 from the center of dilation

at the origin.w’ x’

z’ y’

The distance from the center to each vertex

has been doubled (multiplied times 2)

Page 115: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

w x

z y

Notice: Each image is a result of a dilation by a factor of 2 so they are the same size.

Length was 33 x 2 = 6Length is now 6

Width was 22 x 2 = 4Width is now 4

Page 116: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

A

BC

A’

B’C’

Draw the dilated image of triangle ABC with the center of dilation at the

origin and a scale factor of ½

If you dilate by a factor less than 1, does your shape get

larger or smaller?

SMALLER

Page 117: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

A

BC

Draw the dilated image of triangle ABC with the

center of dilation at vertex A and a scale

factor of ½

A’

B’C’Which vertex did

not change after the dilation?

A and A’ are both at (0,4)

Page 118: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

A

BC

Notice: Each image is a result of a dilation by a factor of ½ so they are the same size.

Page 119: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MA

T H

M’A’

T’ H’

Dilate trapezoid MATH by a factor of 3 around the center

of the figure.

So the height of the figure was 2 units,

what is it now?

6 units

Page 120: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

U

LV

Enlarge LUV by a factor of 1.5 around

the point (0,-1)

L’V’

U’

Where is the center of dilation?

(0,-1)

Page 121: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

U

LV

Enlarge LUV by a factor of 2 around

the origin

Page 122: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

NOW: STUDY FOR YOUR SECOND MIDTERM!

Look over notes and practice problems!

Review formulas you know your struggled with last time!

Remember this is 20% of your grade and a lot of you really need this boost to pass this class! Focus and get to work!

You have ten minutes to study while I hand back papers right now!

Page 123: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

SECOND MIDTERMS!• I am passing them out.

• Calculators are up front! One person may use the calculator at a time!

• Remember to show all work.

• NO TALKING!• When you finish you can get to work on your

make-up work. Be sure to sign up for test corrections so I can make copies.

• If you are talking while people test I will take your make up work and you will keep whatever grade you currently have for good.

Page 124: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW: PULL OUT YOUR PROGRESS REPORTS

Page 125: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

PROGRESS REPORTS!• Be sure you have your test tracking folder. Make sure your test trackers

are filled out.

• Progress reports show homework, class particpation, quizzes and tests.

• You can make up homework and class assignments for full credit.

• Either find them in your notebook and finish them and turn them in or copy down the questions from someone around you or the board examples. If you have to copy you can simply answer the questions and not copy the questions.

• You can do corrections for half credit on quizzes.

• Do corrections on lined sheet of paper and staple them to the back of your quiz. You can also make up a quiz you missed by talking to me.

• You can retake any test objectives you want to do better on in class tomorrow.

• Work on your corrections for the test today and sign up on the side board under the objectives you need copies of. Be sure you study for these. There is no point in re-taking if you don’t learn something new!

• Put any completed work in the turn-in tray! Make today worth it or take the grade you have. If you need something to do come talk to me!

Page 126: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

TESTS!Check your trackers while we work! If you do not have the score listed below for each objective then you need to re-test. Please sign up on the side board so I can have copies ready for you tomorrow! If you don’t sign up I won’t have a test for you!

If you are missing full tests or tests and exams come see me now!

Objective 1: Points, Lines and Planes

Objective 2: Measuring Segments

Objective 3: Angles and Angles Pairs

Objective 4: Distance and Midpoint

Objective 5: Patterns

Objective 6: Conditionals and Biconditionals

Objective 7: Proofs and Missing Angles

Objective 8: Transversals

Page 127: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

PROGRESS REPORTS:

I am handing them out. During this time please remain in your seat and work on your test corrections. Note which objectives you still need to master so you can sign up to retake.

Page 128: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

PROGRESS REPORTS!• Be sure you have your test tracking folder. Make sure your test trackers

are filled out.

• Progress reports show homework, class particpation, quizzes and tests.

• You can make up homework and class assignments for full credit.

• Either find them in your notebook and finish them and turn them in or copy down the questions from someone around you or the board examples. If you have to copy you can simply answer the questions and not copy the questions.

• You can do corrections for half credit on quizzes.

• Do corrections on lined sheet of paper and staple them to the back of your quiz. You can also make up a quiz you missed by talking to me.

• You can retake any test objectives you want to do better on in class tomorrow.

• Work on your corrections for the test today and sign up on the side board under the objectives you need copies of. Be sure you study for these. There is no point in re-taking if you don’t learn something new!

• Put any completed work in the turn-in tray! Make today worth it or take the grade you have. If you need something to do come talk to me!

Page 129: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

WORK TIME:

• I am going to be doing a massive paper handback to start.

• I would be sure to keep all of these together so you can be sure you have correct marks on your progress report.

• After that I will be doing conferences with each of you to get your test scores factored in for your report cards.

• When I call you up please bring your folder and your test tracker.• During this time please be working on your test corrections, quiz

corrections, missing work and book work. If you are wasting this time you will not be given class time to retake this week. If you are all working you will get a review day tomorrow and class re-take time on Thursday.

• If you don’t have an 80% or above on a certain objective you are failing it. So please get to work to fix that score before it becomes permanent.

Page 130: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

DO NOW:• Find your folder in the front of the room

• Look at your test tracker from Test 1 and Test 2 check to see what you need the most work on. If you do not have your Test 2 tracker just wait patiently and Ms. B will be handing them out. If you ask for it before she gets to you you will get it last.

• Find any old quizzes you have and check what you need help with.

• In your Do Now notebook write about at least 3 things from this class so far that you feel like you still need help with.

• If you don’t have any work to look back on just look at old Do Now’s and such to see what you need help with.

Page 131: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MIDTERM REVIEW TIME

• Today is your day to get help on all those loose ends that have been confusing you. This is your last chance to ask questions before the midterm! Make today count!

• Look at the survival guide I passed out. Take 4 minutes to silently read through every topic and really think about where you need the most help. Order the major topics from 1-11 with 1 being the topic you need the most help with and 11 being the topic you feel like you are the master of.

• If you need advice on where you need the most help just look at your test trackers and your Do Now. Where did you do the worst?

Page 132: DO NOW! 1.Give the coordinates for the following points: A B C D E 2. Which line has the following equations: y=x x=2 y=4 A D C E B p w t.

MIDTERM REVIEW TIME!!!

• You now have your own study guide made just for you!

• Around the room there are stations with problems posted on envelopes. Start your time with the station that you need the most help on. (If that station is too crowded just move to another station and come back.)

• Solve the problems and clearly label them on your notes. The answers to the problems are on the inside of the envelopes at each station. Use these to check your answers or see if you’re on the right track. When you are done with them PUT THEM BACK IN THE ENVELOPE!

• Please use these answers before you ask me for help.

• If you don’t feel this is helpful you can work on quiz and test corrections or make up work during this time as well.

• You can work with whomever you’d like and at whatever pace you would like, but you must be working!

• If you can show me full, correct work for 15 practice problems by the end of class you will receive 1 point extra credit on your midterm exam.

• MAKE TODAY WORK FOR YOU!