Find the point, m, that divides segment ab into a ratio of 2: 3 if a is at (0,15) and b is at (20,0)

The ratio has a total of 2+3=5 units, of which 2 correspond to the length of segment AM. The difference of x-coordinates Bx-Ax = 20-0 = 20. 2/5 of that amount is (2/5)*20 = 8, so the x-coordinate of M is

Mx = 8 + Ax = 8 + 0 = 8

The difference of y-coordinates is 0 - 15 = -15. 2/5 of that amount is (2/5)*(-15) = -6, so the y-coordinate of M is

... My = -6 + Ay = -6 + 15 = 9

The point M is (Mx, My) = (8, 9).

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