Transformations Review

What is the angle of rotation if a rotation about the origin maps  $\left(3,\ 1\right)$  to  $\left(1,\ -3\right)$  ?

•  $90\degree$  rotation counterclockwise
  

•  $270\degree$  rotation counterclockwise
  

•  $180\degree$  rotation

•  $270\degree$  rotation clockwise
  

What are the coordinates of the image of  $\left(-3,\ 2\right)$  when the point is reflected across the line  $y=6$  ?

•  $\left(-3,\ 10\right)$  

•  $\left(-3,\ -5\right)$  

•  $\left(3,\ 1\right)$  

•  $\left(2,\ -3\right)$  

What is the image of  $\left(-4,\ -5\right)$  when it is reflected across the line  $y=x$  ?

•  $\left(-4,\ 5\right)$  

•  $\left(-5,\ -4\right)$  

•  $\left(4,\ -5\right)$  

•  $\left(4,\ 5\right)$  

Translate the quadrilateral  $W\left(-2,\ 2\right),\ X\left(-3,\ 3\right),\ Y\left(-6,\ 5\right),\ Z\left(-6,\ 3\right)$ using the transformation  $\left(x-2,\ y+4\right)$  .

•  $W'\left(1,\ 7\right),\ X'\left(0,8\right),\ Y'\left(-3,\ 10\right),\ Z'\left(-3,\ 8\right)$  

•  $W'\left(-5,\ 3\right),\ X'\left(-6,\ 4\right),\ Y'\left(-9,\ 6\right),\ Z'\left(-9,\ 4\right)$  

•  $W'\left(-4,\ 6\right),\ X'\left(-5,\ 7\right),\ Y'\left(-8,\ 9\right),\ Z'\left(-8,\ 7\right)$  

•  $W'\left(4,\ 0\right),\ X'\left(3,\ 1\right),\ Y'\left(0,\ -3\right),\ Z'\left(0,\ 1\right)$  

When the point  $\left(-6,\ 2\right)$  is reflected across the x-axis, what is the resulting image?

•  $\left(6,\ 2\right)$  

•  $\left(2,\ -6\right)$  

•  $\left(-6,\ -2\right)$  

•  $\left(6,\ -2\right)$  

What is the image of the point  $\left(-5,\ 2\right)$  after a  $90\degree$  counterclockwise rotation?

•  $\left(-5,\ -2\right)$  

•  $\left(-2,\ -5\right)$  

•  $\left(2,\ 5\right)$  

•  $\left(5,\ -2\right)$  

 $\Delta JKL$  is translated so that the image of  $K'\left(4,\ -12\right)$  . A composition of reflections across the lines of which equations creates the  same image?

• first $y=-1$  , then  $y=-9$  

• first $y=-5$  , then  $y=-1$  

• first $y=-5$  , then  $y=-9$  

• first $y=-9$  , then  $y=-1$  

After a translation, the image of  $P\left(-3,\ 5\right)$  is  $P'\left(-4,\ 3\right)$  . Identify the image of the point  $\left(1,\ -6\right)$  after this same translation.

•  $\left(4,\ -1\right)$  

•  $\left(-2,\ -5\right)$  

•  $\left(7,\ -8\right)$  

•  $\left(0,\ -8\right)$  

Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.
D:  $\left(x,\ y\right)\rightarrow\left(3x,\ 3y\right)$ 

 $J\left(1,\ 4\right),\ K\left(6,\ 4\right),\ L\left(6,\ 1\right),\ M\left(1,\ 1\right)$  

•  $J'\left(2,\ 8\right),\ K'\left(12,\ 8\right),\ L'\left(12,\ 2\right),\ M'\left(2,2\right)$  

•  $J'\left(3,\ 12\right),\ K'\left(18,\ 12\right),\ L'\left(18,\ 3\right),\ M'\left(3,\ 3\right)$  

•  $J'\left(3,\ 8\right),\ K'\left(18,\ 8\right),\ L'\left(18,\ 2\right),\ M'\ \left(3,\ 2\right)$  

•  $J'\left(2,\ 12\right),\ K'\left(12,\ 12\right),\ L'\left(12,\ 3\right),\ M'\left(2,\ 3\right)$  

Which statement below is false?

• Rigid transformations produce congruent figures.

• Angle measures are preserved through reflections.

• A dilation is a rigid transformation.

• Rotations preserve the distance of side lengths in figures.