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:
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
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:
[tex]R=\left(\dfrac{1(5)+2(-6)}{1+2},\dfrac{1(6)+2(2)}{1+2}\right)[/tex]
[tex]R=\left(\dfrac{5-12}{3},\dfrac{6+4}{3}\right)[/tex]
[tex]R=\left(\dfrac{-7}{3},\dfrac{10}{3}\right)[/tex]
Therefore, the coordinates of point R are [tex]\left(\dfrac{-7}{3},\dfrac{10}{3}\right)[/tex].
