A line segment has endpoints at $(4 ,3 )$ and $(2 ,6 )$ . The line segment is dilated by a factor of $4$ around $(1 ,2 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-19T13:05:07

The new endpoints are $(13,6)$ and $(5,18)$
The length of the line segment is $=sqrt208=14.42$

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

$A=(4,3)$

$B=(2,6)$

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

Let the point $C=(1,2)$

Then,

$vec(CA')=4vec(CA)=4*<4-1,3-2> = <12,4>$

$A'=(12,4)+(1,2)=(13,6)$

Similarly,

$vec(CB')=4vec(CB)=4*<2-1,6-2> = <4,16>$

$B'=(4,16)+(1,2)=(5,18)$

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

$=sqrt((5-13)^2+(18-6)^2)$

$=sqrt(64+144)$

$=sqrt208$

A line segment has endpoints at (4 ,3 )(4 ,3 ) and (2 ,6 )(2 ,6 ). The line segment is dilated by a factor of 4 4 around (1 ,2 )(1 ,2 ). What are the new endpoints and length of the line segment?