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)

(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.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !