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

Answer:

$Q(x,y) = (\frac{-18}{5},\frac{52}{5})$

Step-by-step explanation:

Given

$M = (-10,12)$

$T = (6,8)$

$Ratio = 2:3$ at Q

Required

Determine Q

This can be calculated using line ratio formula;

$Q(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where:

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

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

$m:n = 2:3$

So, we have:

$Q(x,y) = (\frac{2 * 6 + 3 * -10}{2+3},\frac{2 * 8 + 3 * 12}{2+3})$

$Q(x,y) = (\frac{12 -30}{5},\frac{16 + 36}{5})$

$Q(x,y) = (\frac{-18}{5},\frac{52}{5})$

Hence;

The coordinates of Q are:

$Q(x,y) = (\frac{-18}{5},\frac{52}{5})$