Chapter 13.5, Problem 12WE

To determine

To find: the coordinate of $B$

Answer to Problem 12WE

The coordinate of $B$ is $\left(-r,4-s\right)$

Explanation of Solution

Given information: $\left(0,2\right)$ is the midpoint of $\overline{AB}$ , where $A$ has coordinate $\left(r,s\right)$

Calculation:

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

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \left(0,2\right)=\left(\frac{r+x}{2},\frac{s+y}{2}\right)\\ r+x=0\\ x=-r\\ s+y=4\\ y=4-s\\ \Rightarrow \left(-r,4-s\right)\end{array}$