Transformation Compositions

Compositions of Transformations

Multiple Choice

What is translation in geometry?

• Moving a shape or object without changing its size, shape, or orientation.

• Changing the size of a shape or object without moving it.

• Reflecting a shape or object over a line without changing its size or position.

• Rotating a shape or object without changing its size or position.

Multiple Choice

Which transformation flips a figure over a line?

• dilation

• rotation

• reflection

• translation

Match

Match the following

• Dilation

• Translation

• Reflection over x-Axis

• Reflection over y-Axis

• $$180\degree$$ Rotation

(x, y)-->(2x, 2y)

(x, y)-->(x+2, y-2)

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

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

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

• (x, y)-->(2x, 2y)

• (x, y)-->(x+2, y-2)

• (x, y)-->(x, -y)

• (x, y)-->(-x, y)

• (x, y)-->(-x, -y)

Multiple Choice

Which is the algebraic representation for a rotation 180 degrees clockwise?

• (y, x)

• (-y, x)

• (y, -x)

• (-x, -y)

Multiple Choice

Which of the following is the algebraic representation for a translation 7 units left and 6 units up?

• (x + 7, y - 6)

• (x - 7, y + 6)

• (x + 6, y - 7)

• (x - 6, y + 7)

Multiple Choice

If the red triangle is rotated 180 degrees, then reflected over y=2 what is the final image?

• Green Triangle

• Blue Triangle

• Orange Triangle

• Red Triangle

Multiple Choice

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

• 90^o clockwise rotation
• 90^o counter clockwise rotation
• Reflection across the y-axis
• Reflection across the x-axis

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

Describe the transformations that map ABC onto A"B"C"

• translate 5 up and 1 left then reflect over y
• translate 5 down and 1 left, then reflect over y
• reflect over y=x then translate left 8
• reflect over x then rotate 90 clockwise

Multiple Choice

Use the point P(2, –5).  Write the ordered pair for the final location of the given point after completing the transformations in the order listed.

 

Reflection over the x-axis followed by the rule  (x,y) -> (2x, 2y)

• P'(4, -10)

• P'(-4, -10)

• P'(4, 10)

• P'(-4, 10)

Multiple Choice

What is the ordered pair for the final location of P( 2, 3) after this series of transformations? $$\left(x,y\right)\rightarrow\left(x+2,\ y-4\right)$$  then reflected over the  $$y-axis?$$  

• $$P'\left(-4,\ 1\right)$$  

• $$P'\left(-4,\ -1\right)$$  

• $$P'\left(1,\ -4\right)$$  

• $$P'\left(-1,\ -4\right)$$  

Multiple Choice

What is the ordered pair for the final location of P( -7, 3) after this series of transformations? $$\left(x,y\right)\rightarrow\left(x,\ y+3\right)$$  then rotated  $$90\degree$$  clockwise about the origin.

• $$P'\left(-7,\ 6\right)$$  

• $$P'\left(-7,\ -6\right)$$  

• $$P'\left(6,\ -7\right)$$  

• $$P'\left(6,\ 7\right)$$  

Multiple Choice

Identify the transformation from ABCD to A'B'C'D'.

• Translation
• Reflection across the y-axis
• Reflection across the x-axis
• 90^o counter clockwise Rotation