Chapter 8.3, Problem 19E

To determine

The coordinates of the other endpoint.

Answer to Problem 19E

  $\left(3,12\right)$

Explanation of Solution

Given:

The given points are:

  $\begin{array}{l}G\left(5,-6\right)\\ M\left(4,3\right)\end{array}$

Calculation:

The coordinates of midpoint will be:

  $\begin{array}{l}\left(4,3\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \left(4,3\right)=\left(\frac{5+x}{2},\frac{-6+y}{2}\right)\\ \text{Therefore,}\\ \left(\frac{5+x}{2}=4,\frac{-6+y}{2}=3\right)\\ 5+x=8,-6+y=6\\ x=3,y=12\\ \text{hence,}\\ \left(3,12\right)\text{ is the other end point}\text{.}\end{array}$