Chapter 9.1, Problem 51HP

To determine

To proof: The reflection of points $P$ , $Q$ , and $R$ in a line preserves collinearly and between of points.

Answer to Problem 51HP

The reflection of points $P$ , $Q$ , and $R$ in a line preserves collinearly and between of points is proved.

Explanation of Solution

Given information:

The expression $A\left(4,3\right)$ is reflected in a line, its image is $A\text{'}\left(-1,0\right)$ .

Calculation:

Consider a plan for a proof that the reflection of points $P$ , $Q$ , and $R$ in a line preserves collinearly and between of points.

First draw points $P$ , $Q$ , and $R$ so that they are collinear with $Q$ between $P$ and $R$ . Reflect $P$ , $Q$ , and $R$ and connect point $P$ to $P\text{'}$ , $Q$ to $Q\text{'}$ , and $R$ to $R\text{'}$ . Show the resulting quadrilateral congruent. Corresponding parts of congruent figures are congruent.

Hence, proved.