Chapter 13.5, Problem 10CE

To determine

To find: the coordinate of $B$

Answer to Problem 10CE

The coordinate of $B$ is $\left(3,-5\right)$

Explanation of Solution

Given information: $\left(1,-1\right)$ is the midpoint of $\overline{AB}$ , where $A$ has coordinate $\left(-1,3\right)$

Calculation:

The midpoint of the segment that joins points $\left(x_1,y_1\right)\&\left(x_2,y_2\right)$ is the point

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \left(1,-1\right)=\left(\frac{-1+x_2}{2},\frac{3+y_2}{2}\right)\\ -1+x=2;x=3\\ 3+y=-2;y=-5\\ \left(3,-5\right)\end{array}$