M1-T1-L1: Rigid Motion Transformations Homework · 2019. 9. 10. · M1-T1-L3 HW: Translations on Coordinate Plane . REMEMBER: A translation slides a figure along a line a given distance

Name: ___________________________________ Per: _________

M1-T1-L1: Rigid Motion Transformations Homework 1. WRITE: Explain what a conjecture is and how it is used in math.

REMEMBER: If two figures are congruent, all corresponding sides and all corresponding angles have the same measure. (you can use patty paper to help you verify)

2. PRACTICE: Follow the provided steps and complete the table below to help you determine which figuresare congruent to Figure A.

• Make a conjecture about which figures are congruent to Figure A.

• Use patty paper to investigate your conjecture.

• Justify your conjecture by stating how you can move from Figure A to each congruent figure bysliding, flipping, or spinning Figure A.

Figure Congruent to Figure A? (yes or no) How do you move Figure A onto the congruent figure? B No C Yes Spin Figure A and slide onto Figure C D Yes Flip Figure A and slide onto Figure D E Yes Slide Figure A down and to the right onto Figure E F No

M1 Topic 1 Homework Packet

A conjecture is a hypothesis or educated guess that is consistent with what you know but

hasn't been proven yet.

3. STRETCH: The figure on the left was reflected, or flipped,over a line of reflection to create the figure on the right.Determine the location of the line of reflection.

REVIEW:

4. Determine the sum or difference.

a. – 14 + 25 b. – 14 – 25

5. Write the ordered pair for each point plotted on thecoordinate plane provided.

A. __________ B. __________

C. __________ D. __________

6. Calculate the area of each figure. Remember theformula for area of a rectangle is A = 𝑙𝑙 ∙ 𝑤𝑤 and theformula for area of a triangle is A = ½𝑏𝑏 ∙ ℎ.

An extra line has been drawn in to help you break up the shape on part b to make the area easier to find. You will have to break up the shape in a similar way on part a to find the area.

a. b.

Hint: To find the line of reflection… a) Connect the segments of corresponding vertices.b) Draw a line that passes through the midpoints of those lines.

C

D

2

11 –39

(–4, 6) (0, –7)

(4, 0) (8, –3)

186 in2 230 cm2

M1-T1-L3 HW: Translations on Coordinate Plane

REMEMBER: A translation slides a figure along a line a given distance in a given direction. A translation is a rigid motion that preserves the size and shapes of figures.

1. Use the figures shown to the right to complete parts a-c.

a. Describe, in words, the sequence of translations used to moveFigure 1 onto Figure 2.

b. Determine the coordinates of the image of Figure 1 if it istranslated 1 unit horizontally and –8 units vertically. Verify thatthe coordinates you found are correct by drawing the image.Label it Figure 3.

c. State how you determined the coordinates you found in part b.

2. What is true about the relationship between the image and the pre-image after a translation is completed?

3. Use the order of operations to evaluate each expression.

a. −10 + 3(−8) b. −4(−12)

3

4. Describe in words, and then find the rule, given a coordinate of the pre-image and the image.

a. Pre-Image: M (2, –3) b. Pre- Image: P (–5, 1) c. Pre-Image: X (– 4, –9)

Image: M’ (–5, 2) Image: P’ (6, 1) Image: X’ (– 4, –12)

Words: Words: Words:

Rule: Rule: Rule:

3

Left 10 and down 3

(𝟑𝟑,−𝟑𝟑), (𝟒𝟒,𝟎𝟎), (𝟕𝟕,𝟎𝟎), (𝟏𝟏𝟎𝟎,𝟑𝟑)

All of the points in figure 1 moved 1 space right and 8 units down.

The image and the pre-image are congruent. They have the same shape, size and orientation, but in different locations.

–34 16

Left 7 and up 5

(𝒙𝒙 − 𝟕𝟕,𝒚𝒚 + 𝟓𝟓)

Right 11

(𝒙𝒙 + 𝟏𝟏𝟏𝟏,𝒚𝒚)

Down 3

(𝒙𝒙,𝒚𝒚 − 𝟑𝟑)

5. Translate each figure according to the rule or description provided. Be sure to label your new figure with primes.Then state the coordinates of the pre-image and image.

a. four units left and three units up b. (x + 4, y – 2)

6. Write a rule, or write a description, that could be used to find the coordinates of the image given a description.Then use that rule to find the coordinates of the image.

a. left 3 units and up 5 units b. down 8 units c. Words: _________________

Rule: __________________ Rule: ________________ Rule: (x + 4, y – 6)

Pre-Image Image

A(5, 2) A’

B(2, 3) B’

C(4, –2) C’

7. Describe in words, and write a rule, the transformation that has occurred.

a. b.

Words: Words:

Rule: Rule:

8. Point G(2, 7) translates to Point G’(–6, 11). Describe in words how Point G translated to point G’:

The rule that was used would be ( ______ , ______ ).

Using this, Point H (–3, –1) translates to Point H’ ( ___ , ___ ).

Pre-Image Image

D(4, 10) D’

E(2, 6) E’

F(3, – 4) F’

P P’

4

Pre-Image Image

X (–5, 9) X’

Y (–1, 2) Y’

Z(3, –5) Z’

(𝟏𝟏,𝟎𝟎)

(𝟓𝟓,−𝟑𝟑)

(𝟎𝟎,−𝟐𝟐)

(−𝟑𝟑,𝟑𝟑)

(𝟏𝟏,𝟎𝟎)

(−𝟒𝟒,𝟏𝟏)

(−𝟑𝟑,𝟓𝟓)

(𝟏𝟏,𝟓𝟓)

(𝟏𝟏,𝟒𝟒) (−𝟒𝟒,𝟑𝟑)

(𝟏𝟏,𝟑𝟑)

(𝟓𝟓,𝟑𝟑)

(𝟓𝟓,𝟐𝟐)

(𝟎𝟎,𝟏𝟏)

Right 4, down 6 (𝒙𝒙 − 𝟑𝟑,𝒚𝒚 + 𝟓𝟓) (𝒙𝒙,𝒚𝒚 − 𝟖𝟖)

(𝟐𝟐,𝟕𝟕)

(−𝟏𝟏,𝟖𝟖)

(𝟏𝟏,𝟑𝟑)

(𝟒𝟒,𝟐𝟐)

(𝟐𝟐,−𝟐𝟐)

(𝟑𝟑,−𝟏𝟏𝟐𝟐)

(−𝟏𝟏,𝟑𝟑)

(𝟑𝟑,−𝟒𝟒)

(𝟕𝟕,−𝟏𝟏𝟏𝟏)

Right 4, down 4

(𝒙𝒙 + 𝟒𝟒,𝒚𝒚 − 𝟒𝟒)

Left 2, up 1

(𝒙𝒙 − 𝟐𝟐,𝒚𝒚 + 𝟏𝟏)

Left 8, up 4

𝒙𝒙 − 𝟖𝟖 𝒚𝒚+ 𝟒𝟒

−𝟏𝟏𝟏𝟏 𝟑𝟑

M1-T1-L4 HW Reflections on Coordinate Plane

1. a. A reflection is a transformation which ___________ the figure over a given _________.

b. This line is called the .

2. When a point is reflected over the x-axis, the _____ coordinate remains the same, and the ____ coordinatebecomes the opposite sign of the pre-image.

3. When a point is reflected over the y-axis, the _____ coordinate remains the same, and the ____coordinate becomes the opposite sign of the pre-image.

4. Complete each of the following reflections and then name each of the requested coordinates.

a. Reflect over the x-axis b. Reflect over the y-axis c. Reflect over x-axis

Pre- Image Image

P P’

N N’

W W’

L L’

5. When you perform a reflection, what remains the same about the pre-image compared to the image?What is different? (mention side lengths, angle measures, shape, size, orientation, congruent)

6. Various points of a pre-image are provided. Find the coordinates of the image by using the rules learnedin class (without graphing). (remember…think about what changes and what stays the same)

a. Pre-image reflected over x- axis b. Pre-image reflected over y-axis

Pre- Image: 𝐴𝐴 (0, 5) 𝐵𝐵(−3, 0) 𝐶𝐶 (6,−4) Pre- Image: 𝐷𝐷 (2, 5) 𝐸𝐸 (−3, 1) 𝐹𝐹 (0,−4) 𝐺𝐺 (−5, 0)

Image: A’_______ B’ _______ C’ _______ D’ _______ E’ _______ F’ _______ G’ _______

Pre- Image Image

L L’

A A’

I I’

Z Z’

Pre- Image Image

K K’

G G’

L L’

5

flips line Line of reflection

x

x

y

y

(𝟐𝟐,𝟑𝟑)

(𝟒𝟒,𝟐𝟐)

(𝟒𝟒,𝟏𝟏)

(𝟏𝟏,𝟎𝟎)

(𝟐𝟐,−𝟑𝟑)

(𝟒𝟒,−𝟐𝟐)

(𝟒𝟒,−𝟏𝟏)

(𝟏𝟏,𝟎𝟎)

(−𝟑𝟑,−𝟏𝟏)

(−𝟏𝟏,𝟎𝟎)

(𝟎𝟎,−𝟏𝟏)

(−𝟏𝟏,−𝟑𝟑)

(𝟑𝟑,−𝟏𝟏)

(𝟏𝟏,𝟎𝟎)

(𝟎𝟎,−𝟏𝟏)

(𝟏𝟏,−𝟑𝟑)

(−𝟑𝟑,𝟒𝟒)

(𝟎𝟎,𝟎𝟎)

(−𝟐𝟐,−𝟏𝟏)

(−𝟑𝟑,−𝟒𝟒)

(𝟎𝟎,𝟎𝟎)

(-2,1)

They are congruent. They have the same size, shape, angle measures, side lengths, butdifferent orientation and location.

(𝟎𝟎,−𝟓𝟓) (−𝟑𝟑,𝟎𝟎) (𝟔𝟔,𝟒𝟒) (−𝟐𝟐,𝟓𝟓) (𝟑𝟑,𝟏𝟏) (𝟎𝟎,−𝟒𝟒) (𝟓𝟓,𝟎𝟎)

7. Use the coordinate plane to the right. Fill in theprovided table below as you do parts a-d.

a. Plot the points (0, 0), (-4, 8), (-7, 8), and (-7, 5).Connect the 4 points and label this Figure 1.

b. Reflect Figure 1 over the y-axis. Verify your pointsby using the appropriate rule. Label this Figure 2.

c. Reflect Figure 2 over the x-axis. Verify your pointsby using the appropriate rule. Label this Figure 3.

d. Reflect Figure 3 over the y-axis. Verify your pointsby using the appropriate rule. Label this Figure 4.

e. What other reflection could you have done to get Figure 4 instead of reflecting Figure 3 over the y-axis?

Figure 1 Figure 2 Figure 3 Figure 4

(0, 0) (–4, 8),

(–7, 8) (–7, 5)

8. Refer to the coordinate plane below:

Describe how you could move shape 1 to exactly match shape 2 by using one translation and one reflection.

9. Refer to the coordinate plane below:

Describe how you could move shape 2 to exactly match shape 2’ by using one translation and one reflection.

6

(𝟎𝟎,𝟎𝟎) (𝟒𝟒,𝟖𝟖) (𝟕𝟕,𝟖𝟖) (𝟕𝟕,𝟓𝟓)

(𝟎𝟎,𝟎𝟎) (𝟒𝟒,−𝟖𝟖) (𝟕𝟕,−𝟖𝟖) (𝟕𝟕,−𝟓𝟓)

(𝟎𝟎,𝟎𝟎) (−𝟒𝟒,−𝟖𝟖) (−𝟕𝟕,− 𝟖𝟖) (−𝟕𝟕,−𝟓𝟓)

Reflect over the x-axis then translate right 12 and down 3

Reflect over the y-axis then translate up 4

M1-T1-L5 HW: Rotations Practice

1. Graph ∆ABC by plotting the points A(3, 4), B(6, 1), and C(4, 9).Use the origin as your center of rotation. Rotate ∆ABC asdescribed in the table, graph and label the new triangle, andrecord the new vertices.

2. We only learned how to do 90° and 180° rotations. If a problem asked for a 270° rotation clockwise, there are twodifferent ways you could find the image.

1) Turn your paper ______ times clockwise.

2) Turn your paper ______ time counter- clockwise.

3. Verify that a 90° counter-clockwise rotation is the same as a 270° clockwise rotation.

1) Rotate the pre-image 90° counter-clockwise and draw the image.

2) Rotate the original pre-image 270° clockwise. How does this imagerelate to the image you drew in part 1?

REVIEW: Use your knowledge of translations and reflections to answer the following questions.

4. Triangle ABC with coordinates A(2, 4), B(5, –2) , and C(–1, –9) is translated 7 units to the left and 3 units up. Find thecoordinates of the image. (be sure to label them correctly)

5. Triangle ABC with coordinates A(2, 4), B(5, –2) , and C(–1, –9) is reflected over the x-axis. Find the coordinates of theimage. (be sure to label them correctly)

A ______° turn in one direction is the same as a ______° turn in the opposite direction.

7

𝑨𝑨′(−𝟒𝟒,𝟑𝟑) 𝑨𝑨′′(𝟒𝟒,−𝟑𝟑) 𝑨𝑨′′′(−𝟑𝟑,−𝟒𝟒)

𝑩𝑩′(−𝟏𝟏,𝟔𝟔) 𝑩𝑩′′(𝟏𝟏,−𝟔𝟔) 𝑩𝑩′′′(−𝟔𝟔,−𝟏𝟏)

𝑪𝑪′(−𝟗𝟗,𝟒𝟒) 𝑪𝑪′′(𝟗𝟗,−𝟒𝟒) 𝑪𝑪′′′(−𝟒𝟒,−𝟗𝟗)

3 1

270 90

They map (overlap) perfectly.

𝑨𝑨′(−𝟓𝟓,𝟕𝟕) 𝑩𝑩′(−𝟐𝟐,𝟏𝟏) 𝑪𝑪′(−𝟖𝟖,−𝟔𝟔)

𝑨𝑨′(𝟐𝟐,−𝟒𝟒) 𝑩𝑩′(𝟓𝟓,𝟐𝟐) 𝑪𝑪′(−𝟏𝟏,𝟗𝟗)

6. Triangle ABC with coordinates A(2, 4), B(5, –2) , and C(–1, –9) is reflected over the y-axis. Find the coordinates of theimage. (be sure to label them correctly)

7. Calculate each product or quotient.

a. −24.6−6 b. (4.3)(−2.1)

8. Use the given figure to perform the following transformations. Use different colors for each figure to help youdifferentiate the shapes. All rotations use the origin, (0, 0), as the center of rotation. Use patty paper to help you.

0

A. Rotate the original figure 90° clockwise. Label this Figure A.

B. Reflect the original figure over the y-axis. Label this Figure B.

C. Rotate the original figure 90° counter-clockwise. Label this Figure C.

D. Reflect the original figure over the x-axis. Label this Figure D.

E. Rotate the original figure 180°. Label this Figure E.

F. Reflect the original figure over the x-axis, and then reflect that figureover the y-axis. Label this Figure F.

9. How many turns of your patty paper would a 360° rotation be? ______ What would the image look like if youperformed a 360° rotation?

10. Use a piece of patty paper (if necessary) to help you answer the following questions.

A 90° rotation is _____ turn. A 180° rotation is _____ turns. A 270° rotation is _____ turns. A 360° is ______ turns.

450° ______ turns 540° _____ turns 630° ______ turns 720° ______ turns

8

𝑨𝑨′(−𝟐𝟐,𝟒𝟒) 𝑩𝑩′(−𝟓𝟓,−𝟐𝟐) 𝑪𝑪′(𝟏𝟏,−𝟗𝟗)

4.1 –9.03

E & F

B

C

A

D

4

The same as the original figure.

1 2 3 4 5 6 7 8

11. Use the given figures to perform the requested rotations. All rotations for this question use the origin (0, 0) as thecenter of rotation. Find the coordinates of the pre-image and image.

a. rotate 180° b. rotate 90° counter-clockwise c. rotate 90° clockwise

J ___________ J’ ____________ N ___________ N’ ____________ A ___________ A’ ____________

A ___________ A’ ____________ U ___________ U’ ____________ K ___________ K’ ____________

M ___________M’ ____________ M ___________M’ ____________ D ___________ D’ ____________

X ___________X’ ____________ U ___________ U’ ____________

d. rotate 90° clockwise e. rotate 90° counter-clockwise f. rotate 180°

K ___________ K’ ____________ W ___________W’ ____________ P __________P’____________

Z ___________ Z’ ____________ R ___________ R’ ____________ V ___________V’ ____________

M ___________M’ ____________ P ___________ P’ ____________ I ___________ I’ ____________

M ___________M’ ____________

12. In your own words, describe how can you find the coordinates of an image after the pre-image is rotated 180°about the origin.

If point A was (3, –5) and point B was (–2, 7), what would be the coordinates of the image after a 180° rotation?

9

(−𝟒𝟒,−𝟐𝟐)

(−𝟏𝟏,−𝟓𝟓)

(−𝟓𝟓,−𝟒𝟒)

(𝟒𝟒,𝟐𝟐)

(𝟏𝟏,𝟓𝟓)

(𝟓𝟓,𝟒𝟒)

(𝟎𝟎,𝟎𝟎)

(𝟏𝟏,𝟎𝟎)

(𝟑𝟑,−𝟓𝟓)

(𝟎𝟎,−𝟑𝟑)

(𝟎𝟎,𝟎𝟎)

(𝟏𝟏,−𝟏𝟏)

(−𝟓𝟓,−𝟑𝟑)

(−𝟑𝟑,𝟎𝟎)

(𝟎𝟎,−𝟏𝟏)

(−𝟐𝟐,𝟑𝟑)

(𝟎𝟎,𝟑𝟑)

(𝟑𝟑,𝟎𝟎)

(−𝟏𝟏,𝟎𝟎)

(𝟑𝟑,𝟐𝟐)

(𝟑𝟑,𝟎𝟎)

(𝟎𝟎,−𝟑𝟑)

(−𝟓𝟓,𝟑𝟑)

(−𝟐𝟐,𝟐𝟐)

(−𝟓𝟓,𝟎𝟎)

(𝟑𝟑,𝟓𝟓)

(𝟐𝟐,𝟐𝟐)

(𝟎𝟎,𝟓𝟓)

(−𝟒𝟒,𝟏𝟏)

(−𝟏𝟏,𝟎𝟎)

(−𝟑𝟑,−𝟒𝟒)

(−𝟏𝟏,−𝟒𝟒)

(𝟎𝟎,−𝟏𝟏)

(𝟒𝟒,−𝟑𝟑)

(−𝟓𝟓,𝟐𝟐)

(−𝟏𝟏,𝟒𝟒)

(−𝟏𝟏,−𝟏𝟏)

(−𝟒𝟒,−𝟑𝟑)

(𝟓𝟓,−𝟐𝟐)

(𝟏𝟏,−𝟒𝟒)

(𝟏𝟏,𝟏𝟏)

(𝟒𝟒,𝟑𝟑)

You take the opposite of x and the opposite of y for each coordinate.

𝑨𝑨′(−𝟑𝟑,𝟓𝟓) 𝑩𝑩′(𝟐𝟐,−𝟕𝟕)

13. Use the figures to the right to answer the following.

a. Write the coordinates of ∆JKL.

J ___________ K __________ L _____________

b. Describe the rotation used to move ∆JKL onto the shaded figure. Use the origin as the center of rotation. Label the image appropriately.

c. Write the coordinates of ∆J’K’L’ after the rotation done in part b.

J’ ___________ K’ __________ L’ _____________

14. Use the figure to the right.

a. Rotate the figure 90° clockwise. Label this Figure 1 and use primes.

b. Rotate the original figure 180°. Label this Figure 2 and use double primes.

15. Given a triangle with the vertices A (–1, 3), B (4, 8), and C (5, 2). Determine the vertices of each described transformation without graphing.

a. A reflection across the x-axis.

A’ ______________ B’ ______________ C’ ______________

b. A reflection across the y-axis.

A’ ______________ B’ ______________ C’ ______________

c. A translation 5 units horizontally and – 7 units vertically.

A’ ______________ B’ ______________ C’ ______________

16. Simplify by distributing and combining like terms.

a. 2(x + 4) – 3(x – 5) b. 10 – 8(2x – 7)

10

(𝟓𝟓,𝟓𝟓) (𝟔𝟔,𝟗𝟗) (𝟖𝟖,𝟕𝟕)

Rotate 90°CC or 270°C

(−𝟓𝟓,𝟓𝟓) (−𝟗𝟗,𝟔𝟔) (−𝟕𝟕,𝟖𝟖)

1 H’ G’

G’’ K’’

2

J’’ H’’

K’ J’

(−𝟏𝟏,−𝟑𝟑) (𝟒𝟒,−𝟖𝟖) (𝟓𝟓,−𝟐𝟐)

(𝟏𝟏,𝟑𝟑) (−𝟒𝟒,𝟖𝟖) (−𝟓𝟓,𝟐𝟐)

(𝟒𝟒,−𝟒𝟒) (𝟗𝟗,𝟏𝟏) (𝟏𝟏𝟎𝟎,−𝟓𝟓)

−𝒙𝒙 + 𝟐𝟐𝟑𝟑 −𝟏𝟏𝟔𝟔𝒙𝒙 + 𝟔𝟔𝟔𝟔

M1-T1-L6 HW: Transformations Review

1-3: For the triangles in these questions, ∆PQR ≅ ∆JME ≅ ∆DLG.

1. Suppose the vertices of ∆PQR are P(4, 3), Q(–2, 2), and R(0, 0). Describe the translation used to form each triangle.

a. J(0, 3), M(–6, 2), and E(-4, 0) b. D(4, 5.5), L(–2, 4.5), and G(0, 2.5)

2. Suppose the vertices of ∆PQR are P(1, 3), Q(6, 5), and R(8, 1). Describe the rotation used to form each triangle.

a. D(–1, –3), L(–6, –5), and G(–8, –1)

3. Suppose the vertices of ∆PQR are P(12, 4), Q(14, 1), and R(20, 9). Describe the reflection used to form each triangle.

a. J(–12, 4), M(–14, 1), and E(–20, 9) b. D(12, –4), L(14, –1), and G(20, –9)

4. Are the images that result from a translation, rotation, or reflection always, sometimes, or never congruent to the original figure?

5. A reflection over the x-axis, and then over the y-axis would provide an image that is the same as the image created if you performed a _______ ____________________.

6. Use the two congruent triangles to the right.

Complete the congruence statement for the triangles, congruent sides and congruent angles.

∆ABC ≅ ∆______

𝑨𝑨𝑩𝑩���� ≅ _____ 𝑩𝑩𝑪𝑪���� ≅ _____ 𝑪𝑪𝑨𝑨���� ≅ _____

∠𝑨𝑨 ≅ _____ ∠𝑩𝑩 ≅ _____ ∠𝑪𝑪 ≅ _____

11

Left 4 units Up 2.5 units

180°

Over the y-axis Over the x-axis

Always

180° rotation

𝒀𝒀𝒀𝒀𝒀𝒀

𝒀𝒀𝒀𝒀����

∠𝒀𝒀

𝒀𝒀𝒀𝒀����

∠𝒀𝒀

𝒀𝒀𝒀𝒀����

∠𝒀𝒀

7. ∆ABC has coordinates A(1, –8), B(5, –4), and C(8, –9).

a. Graph ∆ABC.

b. What quadrant is ∆ABC in? ____

c. If you performed a translation of ∆ABC up 10 units, what quadrant would the image be in? ____

d. If you performed a reflection of ∆ABC over the y-axis, what quadrant would the image be in? ____

-What if you reflected ∆ABC over the x-axis instead? ____

e. If you performed a 90°counter-clockwise rotation of ∆ABC, what quadrant would the image be in? ____

-What if you rotated ∆ABC 90° clockwise instead? ____

-What if you rotated ∆ABC 180° instead? ____

f. If you performed a 180° rotation of ∆ABC, and then reflected that image over the y-axis, what quadrant would the resulting image be in? ____

g. Reflect ∆ABC over the x-axis. Draw the image and label the new triangle ∆DEF.

- Write congruence statements for the triangles, congruent sides, and congruent angles.

∆ABC ≅ ∆DEF

𝑨𝑨𝑩𝑩���� ≅ 𝑫𝑫𝑫𝑫���� 𝑩𝑩𝑪𝑪���� ≅ 𝑫𝑫𝑬𝑬���� 𝑪𝑪𝑨𝑨���� ≅ 𝑬𝑬𝑫𝑫����

∠𝑨𝑨 ≅ ∠𝑫𝑫 ∠𝑩𝑩 ≅ ∠𝑫𝑫 ∠𝑪𝑪 ≅ ∠𝑬𝑬

8. Identify the transformation used to create ∆XYZ.

a. b.

IV (4) I (1)

III (3)

I (1) I (1)

III (3)

II (2) I (1)

Reflection over the x-axis Translation right 5 and down 11

c. d.

9. Triangle HOP has coordinates H(2, 1), O(–3, 4), and P(5, 7). Draw ∆HOP on the provided coordinate plane. Then determine the coordinates of the image of ∆HOP after each transformation. It is not necessary to draw each resulting image, however using patty paper may help you to find the coordinates.

a. Rotate 90° clockwise.

H’ ___________ O’ ___________ P’ ___________

b. Rotate 180°.

H’ ___________ O’ ___________ P’ ___________

c. Rotate 90° counter-clockwise.

H’ ___________ O’ ___________ P’ ___________

d. Reflect over the x-axis.

H’ ___________ O’ ___________ P’ ___________

e. Reflect over the y-axis.

H’ ___________ O’ ___________ P’ ___________

f. Translate 3 units to the left and 1 unit up.

H’ ___________ O’ ___________ P’ ___________

g. Translate 2 units horizontally and –5 units vertically.

H’ ___________ O’ ___________ P’ ___________

12

13

Rotate 180° Rotate 90° counter-clockwise

Or reflect over the x- and y-axis

(𝟏𝟏,−𝟐𝟐) (𝟒𝟒,𝟑𝟑) (𝟕𝟕,−𝟓𝟓)

(−𝟐𝟐,−𝟏𝟏) (𝟑𝟑,−𝟒𝟒) (−𝟓𝟓,𝟕𝟕)

(−𝟏𝟏,𝟐𝟐) (−𝟒𝟒,−𝟑𝟑) (−𝟕𝟕,𝟓𝟓)

(𝟐𝟐,−𝟏𝟏) (−𝟑𝟑,−𝟒𝟒) (𝟓𝟓,−𝟕𝟕)

(−𝟐𝟐,𝟏𝟏) (𝟑𝟑,𝟒𝟒) (−𝟓𝟓,𝟕𝟕)

(−𝟏𝟏,𝟐𝟐) (−𝟔𝟔,𝟓𝟓) (𝟐𝟐,𝟖𝟖)

(𝟒𝟒,−𝟒𝟒) (−𝟏𝟏,−𝟏𝟏) (𝟕𝟕,𝟐𝟐)

Degrees of a Circle

Use colored pencils to color the circle based on the directions at the bottom of the page and then fill in the blanks around the circle. Your colors will overlap!

A full turn is a very light yellow A ¼ turn is full of purple polka dots A half turn has blue stripes A ¾ turn has green wavy lines Label the degree measurement of a ¼ turn Label the degree measurement of a half turn Label the degree measurement of a ¾ turn Label the degree measurement of a full turn

14

Review Skills Practice 1

A. Integer Practice (http://mathtv.com/topic/algebra/80)

1. −1 ∙ 8 = ________ 2. −13 + 6 = ________ 3. 6 − 18 = ________ 4. −4 ÷ (−2) = ________

B. Fraction Practice (http://mathtv.com/watch/9690001)

5. 3 ∙ 12

= ________ 6. 34∙ 12 = ________ 7. −9 ∙ 1

3= ________ 8. 1

2∙ 8 = ________

9. Use a colored pencil and a ruler to shade ½ of the figure below.

10. Use a colored pencil and a ruler to shade ⅓ of the figure below.

C. Decimal Practice (http://mathtv.com/topic/basic-mathematics/222)

11. 3.5 + 16.25 = ______ 12. 6 + 1.5 = ________ 13. (14)(0.5) = ________ 14. What happens when you multiply a whole number by a decimal less than 1? (ex: 8 ∙ 0.5)

D. Substitution Practice (https://bit.ly/2YQ45gD)

Substitute (replace) the given value for the variable and simplify the expression or ordered pair.

15. 𝑥𝑥 + 3 for 𝑥𝑥 = −5 16. 𝑥𝑥 − 𝑦𝑦 + 6 for 𝑥𝑥 = −2 and 𝑦𝑦 = 3

17. (𝑥𝑥 + 1,𝑦𝑦 + 4) for 𝑥𝑥 = −1 and 𝑦𝑦 = 3

18. 𝑥𝑥2 + 𝑦𝑦 for 𝑥𝑥 = 5 and 𝑦𝑦 = −3

15

−𝟖𝟖

−𝟕𝟕

−𝟏𝟏𝟐𝟐

𝟐𝟐

𝟏𝟏.𝟓𝟓 𝒐𝒐𝒐𝒐 𝟏𝟏 𝟏𝟏𝟐𝟐

𝟗𝟗

−𝟑𝟑

𝟒𝟒

𝟏𝟏𝟗𝟗.𝟕𝟕𝟓𝟓

𝟕𝟕.𝟓𝟓

𝟕𝟕

−𝟐𝟐

𝟏𝟏

(𝟎𝟎,−𝟏𝟏)

𝟐𝟐𝟐𝟐

The whole number gets smaller.

E. Order of Operations Practice (https://youtu.be/ZzeDWFhYv3E)

19. 3𝑥𝑥2 for 𝑥𝑥 = 3 20. 5 − 25 + 2 ∙ 4 − 10 ÷ 2 21. (3 ∙ 52 ÷ 15) − (5 − 22)

F. Coordinate Graphing Practice (https://youtu.be/r16I6LB2YbQ)

22. Write the ordered pairs for each point.

D _______________ E _______________

F _______________ G _______________

23. Graph and label the given points on the coordinate plane below.

A. (−3, 8) B. (0, 0) C. (4, 5) D. (−6, 0) E. (1,−10) F. (2, 0) G. (−7,−7) H. ( 5,−2) J. (0, 5) K. (−2, 3) M. (0,−6)

G. Simplifying Expressions with Variables (http://mathtv.com/topic/algebra/85)

26. 5(4ℎ) 27. 2𝑥𝑥 + 4𝑥𝑥

28. 𝑥𝑥 ∙ 𝑥𝑥 29. 𝑥𝑥 + 𝑥𝑥

Food for Thought

30. Are fractions decimals? Are decimals fractions? How are they similar and how are they different?

16

𝟐𝟐𝟕𝟕

−𝟏𝟏𝟕𝟕

𝟒𝟒

(𝟏𝟏,𝟑𝟑)

(𝟓𝟓,𝟑𝟑)

(𝟕𝟕,−𝟏𝟏)

(𝟏𝟏,−𝟏𝟏)

𝟐𝟐𝟎𝟎𝟐𝟐

𝒙𝒙

𝒙𝒙𝟐𝟐

𝟐𝟐𝒙𝒙

𝑨𝑨

𝑩𝑩

𝑪𝑪

𝑫𝑫

𝑫𝑫

𝑬𝑬

𝑮𝑮

𝑯𝑯

𝑱𝑱

𝑲𝑲

𝑴𝑴