Question

Find the midpoint, M, that divides segment AB into a rstio of 5:3 if A is at (-4, -2) and B is at (4, -10).

a. (1, -7)
b. (2, -7)
c. (2, -8)
d. (1, -8)

Answer 1

Answer:

(1, -7)

Step-by-step explanation:

If we divide a line segment AB from (x₁, y₁) to (x₂, y₂) in the ratio 5:3, the coordinates at the midpoint (M) are  

M = {(5x₂ + 3x₁)/8, (5y₂ + 3y₁)/8}.

A = (-4, -2), B = (4, -10)

M  = {[5×4 + 3(-4)]/8, [5(-10) + 3(-2)]/8}

M  = {(20 – 12)/8, (-50 - 6)/8}

M  = (8/8, -56/8)

M  = (1, -7)

The graph shows M as the green point at (1, -7), and the ratio AM:MB = 5:3.