A line segment has endpoints at $(2, 7)$ $(2 ,7 )$ and $(8, 2)$ $(8 ,2 )$ . The line segment is dilated by a factor of $2$ $2$ around $(1, 1)$ $(1 ,1 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-11T13:11:53

The new end points are $(3, 13)$ $(3,13)$ and $(15, 3)$ $(15,3)$
The length of the line segment is $= \sqrt{244} = 15.6$ $=sqrt244=15.6$

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

$A = (2, 7)$ $A=(2,7)$

$B = (8, 2)$ $B=(8,2)$

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

Let the point $C=(1,1)$

Then,

$vec(CA')=2vec(CA)=2*<2-1,7-1> = <2,12>$

$A'=(2,12)+(1,1)=(3,13)$

Similarly,

$vec(CB')=2vec(CB)=2*<8-1,2-1> = <14,2>$

$B'=(14,2)+(1,1)=(15,3)$

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

$=sqrt((15-3)^2+(3-13)^2)$

$=sqrt(144+100)$

$=sqrt244$

A line segment has endpoints at (2 ,7 )(2,7)(2 ,7 ) and (8 ,2 )(8,2)(8 ,2 ). The line segment is dilated by a factor of 2 22 around (1 ,1 )(1,1)(1 ,1 ). What are the new endpoints and length of the line segment?