Chapter 13.5, Problem 24WE

To determine

To find: the coordinates of a point $T$

Answer to Problem 24WE

The coordinates of a point $T$ is $\left(4,5\right)$

Explanation of Solution

Given information: The points $P\left(2,1\right)\&D\left(7,11\right)$ such that $\frac{PT}{TD}=\frac{2}{3}$

Calculation:

  $\frac{PT}{TD}=\frac{2}{3}$

It means the ratio between $PT:TD$ is $2:3$

  $\begin{array}{l}\Rightarrow \left(\frac{3x_1+2x_2}{2+3},\frac{3y_1+2y_2}{2+3}\right)\\ \Rightarrow \left(\frac{3\left(2\right)+2\left(7\right)}{5},\frac{3\left(1\right)+2\left(11\right)}{5}\right)\\ \Rightarrow \left(\frac{6+14}{5},\frac{3+22}{5}\right)\\ \Rightarrow \left(\frac{20}{5},\frac{25}{5}\right)\\ \Rightarrow \left(4,5\right)\end{array}$

Hence, the coordinate of $T$ is $\left(4,5\right)$