Web view5/14/2017 · Transformations & Rigid Motions (Unit 1) Key Notes. ... Vectors. drawn from pre-image to image and show distance and direction of the slide. T6,

Name: ________________________________ 14-6 Review Unit 1Geometry PD. _____ Date: _______________

Transformations & Rigid Motions (Unit 1)

Key Notes Examples/Further Thinking…

Rigid Motions and transformations- Preserve size, shape and angle measure; only change the position - Rigid Motions produce congruent figures-Translation, Rotation, Reflections are all rigid motions

Notation:Translation: Ta,b

Rotation: Rangle

Reflection: rline of reflection

TranslationsTa,b a → how to move your pre-image left/right

b →how to move your pre-image up/downVectors drawn from pre-image to image and show distance and direction of the slide

T6, -2 moves a figure right 6 and down 2.

Reflections Notation: r1. Graph line of reflection

2. Count how far away each point is on the line and count the opposite going the other way

Special reflections-Point Reflections (LEAP FROG!)

-Line Reflections YOU MUST MEMORIZE: ry=x and ry=-x

ry=x switch x and y coordinatesry= - x switch and negate x and y coordinates.

Special compositions-Perform Compositions from right to left!- Composition of reflections over parallel lines are the same as one translation

T6,0 ° rx-axis 1st: rx-axis 2nd: T6,0

Rotations and more special compositions Notation: REither know your rules, or Rotate paper!Rotate counterclockwise for positive angles, and clockwise for negative angles!- Composition of reflections over perpendicular lines are the same as one rotation

R90°

(turn paper left right turn

and read new coordinates)

Rotational Symmetry Order (How many “clicks” in one full revolution)

360n

to find least amount of degrees to map onto itself

Same formula to finds one exterior angleFor today’s practice, you will work through 5 stations. Check your work as you go!

Station 1: 1-Step Rigid Motions Station 2: Compositions Station 3: Symmetry

Station 4: Congruency Station 5: Error Analysis

Station 1: One Step Rigid Motions

1. What is the image of A(-4,0), B (-1,3) , C(-4,3) under ry= - x? Remember your rules!

2. Graph triangle ABC. A(1, 1), B(4, 5), C(3, 2) and reflect it through point (-2, 1). State the coordinates of the image!

A(1, 1) →

B(4, 5) →

C(3, 2) →

3. Graph Triangle QRS with vertices Q(2,3) R(4, 1) and S(6, 3)and its image after a 270° rotation about the origin.

4. Using appropriate notation, state the rigid motion that is demonstrated below. Be specific.

5. a. Graph and state the coordinates of the image of

A(0,0), B (3,0) , C(3,3) under rx=3?

b. Explain why some of the points didn’t change location.

6. In the diagram, a square is graphed in the coordinate plane.

A reflection over which line does not carry the square onto itself?

7) The image of ∆ ABC after a rotation of 90 degrees clockwise about the origin is ∆≝¿, as shown below.

Station 2: Compositions

8) Consider the following composition: rx-axis ∘ T2,-3. Using that composition, what would be the coordinates of A’, given that A has the coordinates (6, -3)?

9) Below you can see a composition of reflections over lines that are parallel. This same transformation could

have been done as one step. What transformation could have the same result in one-step? _______________________

10) a) Graph and state the coordinates of ∆ A ' ' B ' ' C ' ' , the image of ∆ ABC A(-1,1), B(-5,0) and C(-2,4) after the composition T 2,0o R180 °. Show your work!

b) Complete the sentence: ∆ ABC and ∆ A ' B ' C ' are _____________________ to each other.

11) a) State the composition of transformations shown right.

_________________________________

(*Remember order matters*)

b) Describe the single rigid motion that could have been performed instead of the composition of two reflections over perpendicular lines:

Station 3: Symmetry

12) A regular pentagon is shown in the diagram below. If the pentagon is rotated clockwise around its center, the minimum number of degrees it must be rotated to carry the pentagon onto itself is

1) 54º

2) 72º

3) 108º

4) 360º

13) Consider the regular octagon below:

a) Does the following figure have rotational symmetry?

b) What is the least amount of degrees you must rotate the octagon so that it maps onto itself?

c) What is the order of rotational symmetry of the polygon?

Station 4: Congruency

14) Sketch the reflection of triangleABCin Line m and name it triangle A’B’C’

Line m is the line of reflection. We can also call it the ______________ _______________ of segment AA ’ .

15) The triangle in quadrant 1 was rotated 180o to result its image in quadrant 3. (Shown below)

Use the properties of rigid motions to explain the triangle area congruent.

Station 5: Error Analysis

Look at the student work for #16 - #17.

16)

What type of transformation is shown below? __________

What is the relationship between the pre-image segment and the image segment? Explain why this is true. Be specific!

a) What error did the student make in the explanation? Be specific.

b) Write a thorough and correct explanation below.

17) .Sketch a vector that demonstrates where the translation took place below and DESCRIBE the vector.

a) Is the vector correct? Why or why not?

b) What is the student missing in the explaination?