Chapter 13, Problem 32RP

To determine

To find: The point R that divides AB so that AR: RB is $3:2$ .

Answer to Problem 32RP

Therequired coordinates are $\left(1,\frac{1}{5}\right)$ .

Explanation of Solution

Given:

The given points are $A=\left(8,5\right)$ and $B=\left(7,-3\right)$ .

Calculation:

Consider the given points are $A=\left(8,5\right)$ and $B=\left(7,-3\right)$ .

The ratio of AR: RB is $3:2$ then, the coordinate $x$ is obtained as,

  $\begin{array}{c}x=\frac{2\cdot \left(-8\right)+3\cdot 7}{3+2}\\ =\frac{-16+21}{5}\\ =\frac{5}{5}\\ =1\end{array}$

Coordinate y is obtained as,

  $\begin{array}{c}y=\frac{3\cdot \left(-3\right)+2\cdot 5}{3+2}\\ =\frac{-9+10}{5}\\ =\frac{1}{5}\end{array}$

Thus, the required coordinates are $\left(1,\frac{1}{5}\right)$ .