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# 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 coo

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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.

Jan 18, 2021

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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)

Jan 18, 2021