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((mx_2+nx_1)/(m+n),(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((1(5)+2(-6))/(1+2),(1(6)+2(2))/(1+2)\right)`

`R=\left((5-12)/(3),(6+4)/(3)\right)`

`R=\left((-7)/(3),(10)/(3)\right)`

Therefore, the coordinates of point R are
`\left((-7)/(3),(10)/(3)\right)`.