Question

The endpoints of MN are located at M (-4, 4) and N (2,-2). What are the coordinates of the point that divides MN such that MP: PN is equal to 2: 1?

Answer 1

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

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

Point P divides the line segment MN in 2:1. So,

`P=\left((2(2)+1(-4))/(2+1),(2(-2)+1(4))/(2+1)\right)`

`P=\left((4-4)/(3),(-4+4)/(3)\right)`

`P=\left((0)/(3),(0)/(3)\right)`

`P=(0,0)`

Therefore, the coordinates of the point P are (0,0).