Question

Given A(0, 0) and B(60, 60), what are the coordinates of point M that lies on segment AB such that AM:MB = 2: 3?

Answer 1

The answer is (24, 24).
Solution:
To find the point M that divides segment AB into 2:3 or 2/3 ratio, we determine k by writing the numerator of the ratio over the sum of the terms in the given ratio. Then, we calculate for the coordinates of point M from the slope of the line segment and the coordinates of A = (x1, y1) = (0, 0) and B = (x2, y2) = (60, 60) using the equation
     (x, y) = (x1 + k(x2 - x1), y1 + k(y2 - y1) )
Therefore,
     M = (x, y) = (0 + (2/5)(60 - 0), 0 + (2/5)(60 - 0)) = (24, 24)