Question

A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = \frac{1}{3} \cdot AB$, what are the coordinates for point $C$? Express your answer as an ordered pair.

Answer 1

C = (18, 6)

Explanation:

You have ...

AB : BC = 1 : 1/3 = 3 : 1

(B -A) / (C -B) = 3/1 . . . . . another way to write the distance relation

B -A = 3(C -B) . . . . . . . . . multiply by (C-B)

4B -A = 3C . . . . . . . . . . . add 3B

C = (4B -A)/3 . . . . . . . . . divide by 3 to get an expression for C

C = (4(14, 4) -(2, -2))/3 = (54, 18)/3

C = (18, 6)