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` at Q

Required

Determine Q

This can be calculated using line ratio formula;

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

Where:

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

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

`m:n = 2:3`

So, we have:

`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 are:

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