A line segment has endpoints at $(5, 8)$ $(5 ,8 )$ and $(2, 1)$ $(2 , 1)$ . The line segment is dilated by a factor of $2$ $2$ around $(3, 5)$ $(3 , 5)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-09T13:33:53

The new endpoints are $= (7, 11)$ $=(7,11)$ and $= (1, - 3)$ $=(1,-3)$
The length of the segment is $= \sqrt{232} = 15.2$ $=sqrt232=15.2$

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

$A = (5, 8)$ $A=(5,8)$

$B = (2, 1)$ $B=(2,1)$

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

Let the point $C=(3,5)$

Then,

$vec(CA')=2vec(CA)=2*<5-3,8-5> = <4,6>$

$A'=(4,6)+(3,5)=(7,11)$

Similarly,

$vec(CB')=2vec(CB)=2*<2-3,1-5> = <-2,-8>$

$B'=(-2,-8)+(3,5)=(1,-3)$

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

$=sqrt((1-7)^2+(-3-11)^2)$

$=sqrt(36+196)$

$=sqrt232$

A line segment has endpoints at (5 ,8 )(5,8)(5 ,8 ) and (2 , 1)(2,1)(2 , 1). The line segment is dilated by a factor of 2 22 around (3 , 5)(3,5)(3 , 5). What are the new endpoints and length of the line segment?