Transformational Geometry Review

Transformational Geometry Review

Multiple Choice

The original figure in a transformation.

• Preimage

• Image

• Transformation

• Dilation

Multiple Choice

A figure resulting from a transformation.

• Image

• Preimage

• Transformation

• Dilation

Multiple Choice

A transformation that enlarges or reduces a figure.

• Dilation

• Center of Dilation

• Enlargment

• Reduction

Multiple Choice

A transformation in which a figure is turned about a point.

• Rotation

• Relfection

• Dilation

• Transformation

Multiple Choice

A transformation of a figure that flips the figure across a line.

• Reflection

• Translation

• Rotation

• Dilation

Multiple Choice

A movement (slide) of a figure along a straight line.

• Translation

• Reflection

• Rotation

• Dilation

Multiple Choice

Describe the transformation shown in the graph.

• Translate 4 left and 1 up

• Translate 1 left and 4 up

• Rotate 180 degrees

• Reflect over the x-axis

Multiple Choice

Describe the transformation shown on the graph.

• Reflect over x-axis

• Reflect over y-axis

• Rotate 180 degrees

• Rotate 90 degrees CCW

Multiple Choice

Describe the transformation shown in the graph.

• Reflect over x-axis

• Reflect over y-axis

• Rotate 180 degrees

• Translate 4 units right

Translations

• Right (x +), Left (x-), Up (y+), Down (y-)

• Expressions:

• Translate the following using the transformation (x, y) --> (x+3, y-4) ----- (4, 5)

• Translate the following using the transformation (x, y) --> (2x, y + 4) ------ (5, 6)

• Translate the following using the transformation (4x + 1, y) -------- (2, 3)

• 
  

• 
  

Multiple Choice

Given the point Y at (5, 2), where would the image be after the following translation: (x + 2, y - 7)?

• (7, 7)

• (3, 9)

• (4, -5)

• (7, -5)

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• (x+8, y+4)
• (x-8, y-4)
• (x+4, y+8)
• (x-4, y-8)

Multiple Choice

Write a rule for the translation.

• (x -1, y + 2)

• (x -2, y + 1)

• (x +2, y - 1)

• (x +1, y - 2)

Multiple Choice

Which rule would result in a translation of 2 units left and 3 units up?

• (x, y) → (2x, 3y)

• (x, y) → (x - 2, y + 3)

• (x, y) → (-x, -y)

• (x, y) → (x + 2, y - 3)

Multiple Choice

A quadrilateral with points Q (1.2) , R (4, 5) , S (3, -8), and T (-4, -5) undergoes a translation right 2 and up 3. Which point below is a vertex of the transformed quadrilateral?

• (-5, 5)

• (-2, 2)

• (6, 8)

• (4, 6)

Multiple Choice

The point (4 , 5) undergoes the transformation shown below:

(x, y) ---> (3x + 2, y +4). Which of the following is the transformed coordinate?

• 14, 7

• 5, 8

• 36, 9

• 14, 9

Multiple Choice

Translate the point (10, 12) using the transformation (x+1, 2y-1)

• (11, 26)

• (19, 13)

• (7, 16)

• (11, 23)

Rotations

• To rotate 180 degrees, change the signs of both numbers

• To rotate 90 degrees, switch the x and y values, then change the sign of the second number

Multiple Choice

Triangle B 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

Rotate the point 90^o clockwise about the origin

Point: (-4, 7)

• (7, 4)

• (7, -4)

• (4, -7)

• (-7, -4)

Multiple Choice

The point Z(4, -2) is rotated 180 degrees about the origin. What is the image of Z?

• Z'(2, 4)

• Z'(-4, 2)

• Z'(-2, -4)

• Z'(-4, -2)

Dilations

• Multiply by the scale factor

• If the scale factor is a fraction, divide by the bottom number

• To find scale factor from two points/sides do the new # divided by the original #

Multiple Choice

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

• ½
• ¼
• 4
• 2

Multiple Choice

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor r = 2.

• (2,4.5)
• (-8,-18)
• (8,18)
• (9,4)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Let's Practice

Multiple Choice

The point Z(4, -2) is rotated 180 degrees about the origin.  What is the image of Z?

• Z'(2, 4)
• Z'(-4, 2)
• Z'(-2, -4)
• Z'(-4, -2)

Multiple Choice

Identify the transformation from A to D.

• 90^o Clockwise Rotation
• 180^o Rotation
• 270^o Clockwise Rotation
• 360^o Rotation

Multiple Choice

Which answer shows a reflection across the x-axis?

• d
• c
• b
• a

Multiple Choice

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

• Translated 5 units down and 5 units to the right
• Translated 5 units down and 1 to the right
• Translated 8 units down and 5 units to the right
• Translated 5 units down and 4 units to the right

Multiple Choice

Under a dilation with a scale factor of 4, the ordered pair (0, 3) becomes

• (0, 3)
• (0, 3/4)
• (0, 12)

Multiple Choice

If the ordered pair (3, 6) becomes (1, 2) under a dilation, what was the scale factor?

• 1/3
• 2
• 3
• No way to tell

Multiple Choice

Identify the transformation.

• Reflection across y axis
• Reflection across x-axis
• 180 Rotation
• Translation 2 units down

Multiple Choice

Point G is located at (-4,1). After a sequence of translations, the point was moved 5 units right and 3 units down. What are the coordinates for G''?

• G’' (-1,6)

• G’' (1, -2)

• G'' (-9, -2)

• G'' (-9, 4)

Multiple Choice

If the point located at (3,5) is dilated by a scale factor of 2. What are the new coordinates?

• (3,5)

• (6,10)

• (5,7)

• (1,3)