Question

The coordinates of the endpoint of QS are Q(-9,8) and S(9,-4). Point R is on cue as such that QR:RS Is in the ratio 1:2. What are the coordinates of point R?

Answer 1

R(–3, 4)

Step-by-step explanation:

Let Q(-9,8) and S(9,-4) be the given points and let R(x, y) divides QS in the ratio 1:2.

By section formula,

$R(x, y)=R\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)$

Here, $x_{1}=-9, y_{1}=8, \text { and } x_{2}=9, y_{2}=-4 \text { and } m=1, n=2$

Substituting this in the section formula

$R(x, y)=R\left(\frac{1(9)+2(-9)}{1+2}, \frac{1(-4)+2(8)}{1+2}\right)$  

To simplifying the expression, we get

$\Rightarrow R(x, y)=R\left(\frac{9-18}{3}, \frac{-4+16}{3}\right)$

$\Rightarrow R(x, y)=R\left(\frac{-9}{3}, \frac{12}{3}\right)$

⇒ R(x,y) = R(–3,4)  

Hence, the coordinates of point R is (–3, 4).