Question

A, B and C are collinear, and B is between A and C. The ratio of AB to AC is 2:5 if A is (-6,9) and B is at (-2,3) what are the coordinates of Point C?

Answer 1

C = (4, -6)

Explanation:

The ratio tells you ...

(B-A)/(C-A) = 2/5

Solving for C, we get ...

5(B-A) = 2(C-A) . . . . cross-multiply

5B -5A = 2C -2A . . . eliminate parenthses

5B -3A = 2C . . . . . . add 2A

C = (5B -3A)/2 . . . . divide by 2

Putting in the coordinate values, we find ...

C = ((5(-2)-3(-6))/2, (5(3)-3(9))/2) = (8/2, -12/2)

C = (4, -6)