Given:
The endpoints of MN are located at M (-4, 4) and N (2,-2).
Point P divides the line segment MN such that MP: PN = 2: 1
To find:
The coordinates of point P.
Solution:
Section formula: If a point divides a line segment in m:n, then coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Point P divides the line segment MN in 2:1. So,
[tex]P=\left(\dfrac{2(2)+1(-4)}{2+1},\dfrac{2(-2)+1(4)}{2+1}\right)[/tex]
[tex]P=\left(\dfrac{4-4}{3},\dfrac{-4+4}{3}\right)[/tex]
[tex]P=\left(\dfrac{0}{3},\dfrac{0}{3}\right)[/tex]
[tex]P=(0,0)[/tex]
Therefore, the coordinates of the point P are (0,0).
