Chapter 9.1, Problem 22WE

To determine

To calculate: Find the coordinates.

Answer to Problem 22WE

The coordinates of point Q are $\left(-6,12\right)$ .

Explanation of Solution

Given information: The coordinates of two points P and M are $\left(6,-2\right)$ and $\left(0,5\right)$ respectively.

Formula used: $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation:

Two given points are $P\left(6,-2\right)andM\left(0,5\right)$

Assume $\left(x,y\right)$ as the coordinates of Q,

Hence,

  $\begin{array}{l}\left(\frac{6+x}{2},\frac{-2+y}{2}\right)=\left(0,5\right)\\ \Rightarrow \frac{6+x}{2}=0\\ \Rightarrow 6+x=0\\ \Rightarrow x=-6\\ \therefore x=-6\end{array}$

Now, get the value of y,

  $\begin{array}{l}\Rightarrow \frac{-2+y}{2}=5\\ \Rightarrow -2+y=10\\ \Rightarrow y=10+2\\ \therefore y=12\end{array}$

Therefore, the coordinates of point Q are $\left(-6,12\right)$ .