# Chapter 14: Transformations

Q1.

Copy each figure on graph paper. Then draw the image by reflection in line *k*.

Q1.

Why are the measures of the angles that the initial light ray and the reflected light rays make with the mirrors in the diagram of the periscope on the previous page?

Q1.

Complete each statement for the translation $T:\left(x,y\right)\to \left(x+3,y-1\right)$.

- $T$ Glides points $\underset{\xaf}{?}$ units right and 1 unit $\underset{\xaf}{?}$.
- The image of $\left(4,6\right)$ is $\left(\underset{\xaf}{?},\underset{\xaf}{?}\right)$.
- The pre image of $\left(2,3\right)$ is $\left(\underset{\xaf}{?},\underset{\xaf}{?}\right)$.

Q1.

If function $f:x\to 5x-7$, find the image of 8 and the pre image of 13.

Q1.

Explain why each of the correspondences pictured below is not a one-to-one mapping from set $A$ to set $B$.

Q1.

Complete the following. Assume points *D*, *C*, *U*, *W*, *X*, and *Y* are obtained by reflection in link *k* or *j*.

${R}_{k}$ Stands for $\underset{\xaf}{?}$.

Q10.

Write the coordinates of the image of each point by reflection in,

- The $x-axis$
- The $y-axis$
- The line $y=x$ (Hint: Refer to the Example on page 578)

Point *D*.

Q10.

Complete the following. Assume points *D*, *C*, *U*, *W*, *X*, and *Y* are obtained by reflection in link *k* or *j*.

${R}_{j}:\overrightarrow{ST}\to \underset{\xaf}{?}$

Q10.

Explain how Corollary 2 follows from Theorem 14-1.

Q10.

For each transformation given:

- Plot the three points $A\left(0,4\right)$, $B\left(4,6\right)$, and $C\left(2,0\right)$, and their images $A\text{'}$, $B\text{'}$, and $C\text{'}$ under the transformation.
- State whether the transformation appears to be an isometry.
- Find the pre image of $\left(12,6\right)$.

$G:\left(x,y\right)\to \left(-\frac{1}{2}x,-\frac{1}{2}y\right)$