Question

Find the coordinates of point P that lies along the directed line segment AB in a 2:3 ratio given A (-2, 1), B (3, 4).

Answer 1

`P(x,y) = (0,(11)/(5))`

Explanation:

Given

`A = (-2,1)`

`B = (3,4)`

`m:n = 2:3`

Required

Determine the coordinates of P

The coordinate of a point when divided into ratio is:

`P(x,y) = ((mx_2 + nx_1)/(m + n),(my_2 + ny_1)/(m + n))`

Where

`(x_1,y_1) = (-2,1)`

`(x_2,y_2) = (3,4)`

`m:n = 2:3`

This gives:

`P(x,y) = ((2 * 3 + 3 * -2)/(2 + 3),(2 * 4 + 3 * 1)/(2 + 3))`

`P(x,y) = ((6 - 6)/(5),(8 + 3)/(5))`

`P(x,y) = ((0)/(5),(11)/(5))`

`P(x,y) = (0,(11)/(5))`