Question

Find B on AC such that the ratio of AB to BC is 3:2. A (4, 2) and C (-6, - 13).

Answer 1

B(-2, -7)

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).