Chapter 8, Problem 19RP

To determine

To find:The coordinates of Q point in the figure.

Answer to Problem 19RP

The coordinates of Q are ( − 13, 0)

Explanation of Solution

Given information:

PQ = 30 units

Formula used:

Congruency of triangles

Ratio of corresponding sides are equivalent

Calculation:

In Triangles QPR and RPS. We have

  $\begin{array}{l}\angle \text{QPR}=\angle \text{RPS}\mathrm{......}given\\ \text{RS}=\text{RS}\mathrm{.......}\text{common side}\\ \angle \text{PRQ=}\angle \text{PRS}\mathrm{.....}\text{angle formed by common side}\\ \therefore \Delta \text{QPR}\cong \Delta \text{RPS}\mathrm{.....}\text{ASA criteria is satisfied}\end{array}$

Thus, we have

  $\begin{array}{l}\frac{\text{QR}}{\text{PQ}}=\frac{\text{RS}}{\text{PS}}\\ \Rightarrow \frac{\text{QR}}{\text{30}}=\frac{\text{8}}{\text{24}}\\ \Rightarrow \text{QR}=30\times \frac{\text{8}}{\text{24}}=10\text{units}\end{array}$

  $\therefore$ Point Q is 13 points from origin

Hence,

Coordinates of Q = (− 13, 0)