Question

9. Find the coordinates of point C along line segment AE with A(-2,-4) and

E(8.1), so that the ratio of AC to CE is 3 to 2. *

Answer 1

`C = (4,-1)`

Explanation:

Given

`A = (-2,-4)`

`E = (8,1)`

`AC:CE = 3:2`

Required

Determine the coordinates of C

This is calculated as follows;

`C = ((mx_2 + nx_1)/(m+n),(my_2 + ny_1)/(m+n))`

Where:

`(x_1,y_1) = (-2,-4)`

`(x_2,y_2) = (8,1)`

`m:n = 3:2`

So, we have:

`C = ((3 * 8 + 2 * -2)/(3+2),(3 * 1 + 2 * -4)/(3+2))`

`C = ((24 -4)/(5),(3-8)/(5))`

`C = ((20)/(5),(-5)/(5))`

`C = (4,-1)`