Exercise 3 Page 163

Let's draw an arbitrary figure in a coordinate plane.

To perform a reflection you first need a line of reflection. Such a line is used in the same way as a mirror. We are free to choose whatever line of reflection we want, but to make things easy, lets show a reflection in the $y\text{-}$axis. Since none of the points are on the $y\text{-}$axis, the $y\text{-}$axis will form a perpendicular bisector to $\overline{A{A}^{\prime }},$ $\overline{B{B}^{\prime }},$ and $\overline{C{C}^{\prime }}.$

This means that the segments between the image and preimage vertices will be horizontal. Using these horizontal segments, we measure the distance between each vertex, $A$, $B$, and $C$, and the $y\text{-}$axis. We then replicate those distances on the other side of the $y\text{-}$axis to find $A^{\prime },$ $B^{\prime },$ and $C^{\prime }$ respectively.