A line segment has endpoints at $(7 ,6 )$ and $(5 ,2 )$ . The line segment is dilated by a factor of $4$ around $(4 ,3 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-12T10:00:34

The new end points are $(16.15)$ and $(8,-1)$
The length of the new segment is $=sqrt320=17.9$

Let the endpoints of the segment be $A$ and $B$

$A=(7,6)$

$B=(5,2)$

Let the endpoints after dilatation be $A'$ and $B'$

Let the point $C=(4,3)$

Then,

$vec(CA')=4vec(CA)=4*<7-4,6-3> = <12,12>$

$A'=(12,12)+(4,3)=(16,15)$

Similarly,

$vec(CB')=4vec(CB)=4*<5-4,2-3> = <4,-4>$

$B'=(4,-4)+(4,3)=(8,-1)$

The length of the segment $A'B'$ is

$=sqrt((16-8)^2+(15+1)^2)$

$=sqrt(64+256)$

$=sqrt320$

A line segment has endpoints at (7 ,6 )(7 ,6 ) and (5 ,2 )(5 ,2 ). The line segment is dilated by a factor of 4 4 around (4 ,3 )(4 ,3 ). What are the new endpoints and length of the line segment?