khan academy Divide line segments

Question

Find the coordinates of point B on AC such that the ratio of ab to ac is 1:3 a(-2,4) c(4,7)

Answer 1

Point A: (-2,4)

Point C: (4,7)

Given Point B is at a point that is 1/3 the length of AC (AB/BC =1/3)

X Direction: A→C = 4 - (-2) = 6

Y Direction: A→C = 7 - 4 = 3

Therefore:

B = A + 1/3 AC

B = (-2 + (1/3)(6), 4 + (1/3)(3))

B = (0,5)