Find the point, M, that divides segment AB into a ratio of 3:2 if A is at (0, 15) and B is at (20, 0).

Answer 1

Let M be (x,y)
Make a sketch , draw two right-angled triangles, with hypotenuse AM = 3 and hypotenuse MB = 2
then use similar triangle ratios.

for the x:
(x-0)/20-x) = 3/2
2x = 60-3x
5x = 60
x = 12

for the y:
(15-y)/(y-0) = 3/2
3y = 30 - 2y
5y = 30
y = 6

M is (12,6)

or:
the x of M is 3/5 of the way to 20 ---> 12
the y of M is 2/5 of the way to 15 ----> 6