Chapter 8.5, Problem 30PSC

To determine

To find the coordinates of point R and Q.

Answer to Problem 30PSC

The coordinates of $R=\left(9,3\right)$ and $Q=\left(9,7\right)$ .

Explanation of Solution

Given information:

  $\overline{BR}$ is parallel to y axis.

  $\overline{AR}$ is parallel to x axis.

Point P divides $\overline{AB}$ in ratio $\frac{2}{3}$ .

Formula used:

The below properties are used:

If both angles are right angles, then they are congruent.

If two triangles are similar, then there corresponding sides are proportional.

Calculation:

  

R=(9,3)

By reflexive property, we get

  $\angle B\cong \angle B$

If both angles are right angles, then they are congruent.

  $\angle BQP\cong \angle BRA$

  $\Delta BQP~\Delta BRA$

If two triangles are similar, then there corresponding sides are proportional.

  $\begin{array}{l}\therefore \frac{BQ}{BR}=\frac{BP}{BA}\\ \frac{BQ}{10}=\frac{3K}{5K}\\ 30K=5K(BQ)\\ 6=BQ\\ BQ=6\end{array}$

Thus, $Q=\left(9,7\right)$