91Ó°ÊÓ

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

$R_k:\stackrel{→}{BC}→\underset{¯}{?}$

For each transformation given:

1. 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.
2. State whether the transformation appears to be an isometry.
3. Find the pre image of $\left(12,6\right)$.

$H:\left(x,y\right)→\left(-x,-y\right)$

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

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

Point B.

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

$R_k:∠STU→\underset{¯}{?}$

Does the polar map preserve or distort distance?

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

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

Point C.

Explain how Corollary I follows from Theorem 14-1.

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

$R_j\left(S\right)=\underset{¯}{?}$

For each transformation given:

1. 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.
2. State whether the transformation appears to be an isometry.
3. Find the pre image of $\left(12,6\right)$.

$M:\left(x,y\right)→\left(12-x,y\right)$