Directed line segment DE has endpoints D(-4,-2) and E(1,8). Point F divides DE such that DF:FE is 2:3. What are the coordinates of F?

A. (-3,0)
B.(-2,2)
C(-1,4)
D.(2,4)

in x first

Ex - Dx = 1 - -4 = 5
if ratio is 2/3 then DF/DE = 2/5 and FE/DE =3/5
so Fx = Dx + 2/5 *5 = -4+2 = -2

Ey - Dy = 8 - -2 = 10
so Fy =Dy +2/5 * 10 = -2+4 = +2
so
(-2 , +2)

Thank you so much!

You are welcome.

To find the coordinates of point F, we need to divide the line segment DE into two parts with a ratio of 2:3.

First, we calculate the differences in x-coordinates and y-coordinates between points D and E:
Δx = E_x - D_x = 1 - (-4) = 5
Δy = E_y - D_y = 8 - (-2) = 10

Next, we multiply the ratio (2:3) with the differences:
DF_x = (2/5) * Δx = (2/5) * 5 = 2
DF_y = (2/5) * Δy = (2/5) * 10 = 4

Finally, we add DF to the coordinates of point D to find the coordinates of F:
F_x = D_x + DF_x = -4 + 2 = -2
F_y = D_y + DF_y = -2 + 4 = 2

The coordinates of point F are (-2, 2), so the answer is B.