Question

What are the coordinates of R on segments QS such that the ratio is 1:2. Q(-6,2) S(5,6)

Answer 1

Given:

The endpoints of a line segment QS are Q(-6,2) and S(5,6).

Point R divides the line segment QS in 1:2.

To find:

The coordinates of point R.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are:

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

It is given that the endpoints of a line segment QS are Q(-6,2), S(5,6) and point R divides the line segment QS in 1:2. So, the coordinate of point R are:

$R=\left(\dfrac{1(5)+2(-6)}{1+2},\dfrac{1(6)+2(2)}{1+2}\right)$

$R=\left(\dfrac{5-12}{3},\dfrac{6+4}{3}\right)$

$R=\left(\dfrac{-7}{3},\dfrac{10}{3}\right)$

Therefore, the coordinates of point R are $\left(\dfrac{-7}{3},\dfrac{10}{3}\right)$.