Foundations of Math II Exam Review: Rigid Transformations

By Susan Joyce

Foundations of MathII Exam Review - Rigid Transformations

Translation

• Slides a figure on the coordinate plane

Multiple Choice

Triangle EFG will be translated 4 units to the right and 3 units down. What will be the coordinates of G'?

• (3,-2)

• (3,4)

• (2,-3)

• (2,-2)

Multiple Choice

Triangle JKL will be translated 8 units to the right and 6 units down. What will be the coordinates of J'?

• (2,-6)

• (4,-4)

• (6,-4)

• (6,-8)

Open Ended

Let's discuss.

1. What is the same for each point?

2. What is different for each point?

3. What is the rule for reflecting over the x-axis?

Reflections over the x-axis:

(x,y) -> (x,-y)

Multiple Choice

What are the coordinates of B' after a reflection over the x-axis?

• (-2,4)

• (4,-2)

• (-2,-4)

• (2,4)

Fill in the Blanks

A preimage has point A located at (5,3). What are the coordinates for point A' after reflecting over the x-axis. (Write your answer without spaces.)

Open Ended

10. Let's Discuss.

1.What is the same for each point?

2.What is different for each point?

3.What is the rule for reflecting over the y-axis?

Reflections over the y-axis

(x,y) -> (-x,y)

Multiple Choice

What are the coordinates for C' after a reflection over the y-axis?

• (1,2)

• (-1,-2)

• (2,1)

• (-1,2)

Multiple Choice

A figure has _______ symmetry when a line (or lines) divide the shape into two equal parts.

• Line

• Rotational

• Point

​Some text here about the topic of discussion.

​Reflection Across y = x

When you reflect a shape across the line y = x, change the x and y coordinates.

​

​(4,9) ---> (9, 4)

​Some text here about the topic of discussion.

​Reflection Across y = -x

​When you reflect a shape across the line y = -x, change the x and y coordinates, and change the signs to the opposite signs.

​(8, 2) ---> (-2, -8)

Multiple Choice

How many lines of symmetry does the flower have?

• 2
• 3
• 6
• 9

Multiple Choice

How many lines of symmetry does this figure have?

• 1

• 3

• 5

• 7

Rotation

• turning shapes about the origin

Multiple Choice

Triangle EFG will be rotated 90 degrees counterclockwise about the origin. What will be the coordinates of E'?

• (-2,-1)

• (-1,-2)

• (1,-2)

• (2,1)

Multiple Choice

Rotate the point (7,8) around the origin 90 degrees counter clockwise. State the image of the point.

Rule: (x, y) ---- ( -y, x)

• (-7,-8)

• (8,-7)

• (-8,7)

• (8,7)

Multiple Choice

Rotate the point (5,5) around the origin 180 degrees counterclockwise. State the image of the point.

Rule: (x, y) ---- ( -x, -y)

• (5,-5)

• (5,5)

• (-5,-5)

• (-5,5)

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 
• 180 degrees
• 90 degrees clockwise

Multiple Choice

If you were to rotate ABCD 180° about the origin, what would the coordinates of B' be?

• (0, 0)
• (-6, -5)
• (-1, 3)
• (-6, 2)

Multiple Choice

Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Triangle D is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A
• B
• C
• D

Multiple Choice

What is the order of rotational symmetry for the shape below?

• 0
• 1
• 2
• 3

Multiple Choice

What is the order of rotation in the recycling symbol?

• 1
• 2
• 3
• 1,000

Multiple Choice

Find the order of rotational symmetry in this shape.

• 4

• 8

• 7

• 6

Multiple Choice

Identify the smallest angle of rotation that maps the image to itself.

• 90°
• 180°
• 45°
• 60°

​Some text here about the topic of discussion.

​Hint for Composite Transformations

Use the rules for each type of transformation to determine the new coordinates.

Rotate (3,4) 90^o CCW about origin and then translate T_(2,-5)

​_{(3, 4) Rotate 90 CCW--> (-4, 3)}

​(-4, 3) T_(2,-5) ---> (-2, -2)

Multiple Choice

• F

• G

• H

• J

Multiple Choice

Determine the image of A after it's first translated by the rule

(x, y) → (x − 4, y + 1)

and is then reflected over the y-axis.

• (-1, 4)

• (1, 4)

• (4, -1)

• (-4, -1)

Multiple Choice

In doing composite transformations, the order that you do them doesn't matter

• True

• False

Multiple Choice

R_x-axis  $$\circ$$  R_y-axis A(7, -3), Where is A"

• (-3, 7)

• (3, -7)

• (-7, 3)

• (-7, -3)

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflect across the x-axis and then rotate -90 degrees cw around the origin

• Rotate 90 degrees cw around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees ccw about the origin.

Multiple Choice

What is the sequence of transformations?

• Reflect over the y then reflect over the x
• Reflect over the x then reflect over the y
• Translate 4 units then rotate 90˚
• Rotate 90˚ then reflect over the x

Multiple Choice

(2, 6) -- Translate up 3, left 1 and rotate 180°

• (-1,-9)

• (1, -9)

• (5,5)

• (-5,5)