#### Exercise 4

Chapter 3, Section 3-1, Page 108
ISBN: 9780328931583

Solution

Verified
Step 1
1 of 5

To find what reflection rule maps triangle to its image, we must clearly $\textbf{define the line of reflection}$.

Be certain that the line of reflection is $\textbf{perpendicular bisector of segments between preimage and image points.}$

$\boxed{\quad \text{\textbf{a.}}\quad}$

$\textbf{Step 1:}$

Write the coordinates of preimage and image:

$C(3,8) \quad D(5,12) \quad E(4,6)$

$C'(-8,-3) \quad D'(-12,-5) \quad E'(-6,-4)$

$\textbf{Step 2:}$

Find the midpoints of the segment connecting two pairs of corresponding points.

Midpoint of $\overline{CC'}$:

$\left( \frac{3+(-8)}{2},\frac{8+(-3)}{2}\right)=\left( \frac{-5}{2},\frac{5}{2}\right)=(-2.5,2.5)$

Midpoint of $\overline{EE'}$:

$\left( \frac{4+(-6)}{2},\frac{6+(-4)}{2}\right)=\left( \frac{-2}{2},\frac{2}{2}\right)=(-1,1)$

$\textit{(Remember that the line is uniquely determined by two points.\\ Therefore, only 2 midpoints is sufficient to calculate.)}$