Chapter 9.5, Problem 48E

To determine

Tofind:Coordinates of point B

Answer to Problem 48E

  $B\left(4,1\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}A\left(-2,2\right)\\ M\left(1,1\frac{1}{2}\right)\end{array}$

Concept Used:

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

Calculation:

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

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

  $\begin{array}{l}\frac{-2+x_2}{2}=1\text{ and }\frac{2+y_2}{2}=\frac{3}{2}\\ -2+x_2=\left(1\right)\text{2 and 2}+y_2=\left(\frac{3}{2}\right)2\\ x_2=2+2\text{ and }{y}_2=3-2\\ x_2=4\text{ and }{y}_2=1\end{array}$

Therefore, point B will be $B\left(4,1\right)$