Answer:
B(-2, -7)
Step-by-step explanation:
The ratio requirement means ...
(B-A)/(C-B) = 3/2
2(B-A) = 3(C-B) . . . . cross multiply
2B -2A = 3C -3B . . . eliminate parentheses
5B = 2A +3C . . . . . . add 3B+2A
B = (2A +3C)/5 . . . . divide by 5
Now that we have a formula for B, we can fill in the given point values:
B = (2(4, 2) +3(-6, -13))/5 = (8-18, 4-39)/5 = (-10, -35)/5 = (-2, -7)
The coordinates of B are (-2, -7).
