Question

Given directed line segment QS , find the coordinates of R

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ($x_1,y_1$) and B($x_2,y_2$) is given by the formula:

$x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1$

If point Q is at ($x_1,y_1$) and S at ($x_2,y_2$)  and R(x, y) divides QS in the ratio QR to RS is 3:5, The coordinates of R is:

$x=\frac{3}{3+5}(x_2-x_1)+x_1=\frac{3}{8}(x_2-x_1)+x_1\\ \\y=\frac{3}{3+5}(y_2-y_1)+y_1=\frac{3}{8}(y_2-y_1)+y_1$

Let us assume Q(−9,4) and S(7,−4)

$x=\frac{3}{8}(7-(-9))+(-9)=\frac{3}{8}(16)-9=-3\\\\y=\frac{3}{8}(-4-4)+4=\frac{3}{8}(-8)+4=1$