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# A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = \frac{1}{3} \cdot AB$,

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what are the coordinates for point $$c$$ ? Express your answer as an ordered pair.

Dec 8, 2020

#1
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New point  C =

[  14 + (1/3)(14-2)  ,  2 + (1/3)(4  - - 2) ]  =

[ 14 + (1/3) (12)  ,    2  +  (1/3)(6)  ]  =

[ 14  + 4 , 2 + 2  ]  =

( 18 , 4)   Dec 8, 2020
#2
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Thanks for trying but it is incorrect

Dec 8, 2020
#3
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The answer to this problem is actally 18,6

Dec 8, 2020
#4
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Sorry....I  made a slight mistake...it should be

[  14 + (1/3)(14-2)  ,  4 + (1/3)(4  - - 2) ]  =

[ 14 + 4,  4 + 2  ]  =

(18,  6)

THX for the correction   !!!!   CPhill  Dec 8, 2020
edited by CPhill  Dec 8, 2020
#5
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From A to B, the x coordinate increases by 12 and the y coordinate increases by 6.  If we continue on for 1/3 of this distance, we will add $1/3*12 = 4$ to the x coordinate and $1/3*6 =2$ to the y coordinate, to get $C = (14+4,4+2) = (18,6)$

Dec 11, 2020