Chapter 9.1, Problem 23WE

To determine

To calculate: Find the coordinates.

Answer to Problem 23WE

The coordinates of point Q are $\left(-h,-y\right)$ .

Explanation of Solution

Given information: The coordinates of two points P and M are $\left(h,k\right)$ and $\left(0,0\right)$ respectively.

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

Calculation:

Two given points are $P\left(h,k\right)andM\left(0,0\right)$ .

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

Hence,

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

Now, get the value of y,

  $\begin{array}{l}\Rightarrow \frac{k+y}{2}=0\\ \Rightarrow k+y=0\\ \Rightarrow y=-k\\ \therefore y=-k\end{array}$

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