Chapter 8.5, Problem 14PSA

To determine

To find coordinates of a point.

Answer to Problem 14PSA

The coordinates of a point are (0, 18).

Explanation of Solution

Given information:

  $\overleftrightarrow{PT}$ bisects $\angle RPQ$

  $\begin{array}{l}PR=30,\\ PQ=24\end{array}$

Formula used:

The below theorem is used:

Angle bisector theorem states that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

Calculation:

  

It is given that,

  $\overleftrightarrow{PT}$ bisects $\angle RPQ$

  $\begin{array}{l}PR=30,\\ PQ=24\end{array}$

Using Angle Bisector Theorem, we get

  $\begin{array}{l}\frac{RT}{QT}=\frac{PR}{PQ}\\ QT=8\\ \frac{RT}{8}=\frac{30}{24}\\ 24(RT)=240\\ \therefore RT=\frac{240}{24}=10\\ \therefore R(0,18)\end{array}$