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)

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)