Chapter 13.5, Problem 10WE

To determine

To find: the coordinate of $B$

Answer to Problem 10WE

The coordinate of $B$ is $\left(4,10\right)$

Explanation of Solution

Given information: $\left(4,4\right)$ is the midpoint of $\overline{AB}$ , where $A$ has coordinate $\left(4,-2\right)$

Calculation:

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

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \left(4,4\right)=\left(\frac{4+x}{2},\frac{-2+y}{2}\right)\\ 4+x=8\\ x=8-4=4\\ -2+y=8\\ y=8+2=10\\ \Rightarrow \left(4,10\right)\end{array}$