Question

Given the points M (-10, 12) and T(6,8), find the coordinates of the point Q on a directed line segment MT that partitions MT in the ration 2:3.

Answer 1

`Q(x,y) = ((-18)/(5),(52)/(5))`

Explanation:

Given

`M = (-10,12)`

`T = (6,8)`

`Ratio = 2:3`

Required

Determine the coordinate of Q

The question will be answered using the following line ratio formula

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

Where

`m:n = 2:3`

`(x_1,y_1) = (-10,12)`

`(x_2,y_2) = (6,8)`

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

`Q(x,y) = ((2 * 6 + 3 * -10)/(2+3),(2 * 8 + 3 * 12)/(2+3))`

`Q(x,y) = ((12 - 30)/(5),(16+36)/(5))`

`Q(x,y) = ((-18)/(5),(52)/(5))`

Hence,, the coordinates of Q is

`Q(x,y) = ((-18)/(5),(52)/(5))`