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

Answer:

$C = (4,-1)$

Step-by-step explanation:

Given

$A = (-2,-4)$

$E = (8,1)$

$AC:CE = 3:2$

Required

Determine the coordinates of C

This is calculated as follows;

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

Where:

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

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

$m:n = 3:2$

So, we have:

$C = (\frac{3 * 8 + 2 * -2}{3+2},\frac{3 * 1 + 2 * -4}{3+2})$

$C = (\frac{24 -4}{5},\frac{3-8}{5})$

$C = (\frac{20}{5},\frac{-5}{5})$

$C = (4,-1)$