Chapter 13.5, Problem 11WE

To determine

To find: the coordinate of $B$

Answer to Problem 11WE

The coordinate of $B$ is $\left(9,5\right)$

Explanation of Solution

Given information: $\left(5,1\right)$ 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

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \left(5,1\right)=\left(\frac{1+x}{2},\frac{-3+y}{2}\right)\\ 1+x=10\\ x=10-1=9\\ -3+y=2\\ y=2+3=5\\ \Rightarrow \left(9,5\right)\end{array}$