Question

A B and C are collinear, and B is between A and C. The ratio of AB to AC is 2:7. If A is at (0,-8) and B is (2,-4), what are the coordinates of point C?

Answer 1

C = (7, 6)

Explanation:

The problem statement tells us the relation between the points is ...

(B-A)/(C-A) = 2/7

7(B -A) = 2(C -A) . . . . . . multiply by 7(C-A)

7B -7A +2A = 2C . . . . . add 2A

C = (7B -5A)/2 . . . . . . . divide by 2

C = (7(2, -4) -5(0, -8))/2 = (14, 12)/2 . . . . . fill in the values of A and B

C = (7, 6)