Chapter 9.5, Problem 45E

To determine

Tofind:Coordinates of point B

Answer to Problem 45E

  $B\left(-8,0\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}A\left(0,6\right)\\ M\left(-4,3\right)\end{array}$

Concept Used:

Midpoint of two points - $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation:

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \Rightarrow \left(-4,3\right)=\left(\frac{0+x_2}{2},\frac{6+y_2}{2}\right)\end{array}$

Comparing L.H.S with R.H.S, we get-

  $\begin{array}{l}\frac{0+x_2}{2}=-4\text{ and }\frac{6+y_2}{2}=3\\ x_2=\left(-4\right)\text{2 and }6+y_2=\left(3\right)2\\ x_2=-8\text{ and }6+y_2=6\\ x_2=-8\text{ and }{y}_2=6-6\\ x_2=-8\text{ and }{y}_2=0\end{array}$

Therefore, point B will be $B\left(-8,0\right)$