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.
A = (2, -2) B =(14,4)
BC = (1/3) AB
We can find the coordinates of C thusly :
( 14 + (1/3) ( 14 -2) , 4 + (1/3)(4 - -2) ) =
(14+ 12/3 , 4 + 6/3) =
(14 + 4 , 4 + 2) =
(18, 6)
