Given the points C(-1, -5) and D(-7, 11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3

Question

Given the points C(-1, -5) and D(-7, 11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3

I need the work also

Answer 1

5/8 x 6 = (5/8)(-6) = -15/4. -15/4 -1 = -19/4 = the x coordinate

5/8 x 16 = 10. 10 -5 = 5 = the y coordinate

(-4.75, 5) is point E

Answer 2

Let point E(x,y). CE = <x + 1, y + 5>; ED = <- 7 - x, 11 - y>; CE/ED = 5/3; 3CE = 5ED;

3<x + 1, y + 5> = 5<- 7 - x, 11 - y>; 3x + 3 = - 35 - 5x; 8x = - 38; x = - 19/4;

3y + 15 = 55 - 5y; 8y = 40; y = 5. So, E(- 19/4, 5>