A line segment has endpoints at $(3, 2)$ $(3 ,2 )$ and $(6, 8)$ $(6 ,8 )$ . The line segment is dilated by a factor of $4$ $4$ around $(1, 3)$ $(1 ,3 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2017-03-19T07:00:49

The new end points are $(9, - 1)$ $(9,-1)$ and $(21, 23)$ $(21,23)$
The length of the line segment is $= 26.8$ $=26.8$

Let $A B$ $AB$ be the line segment

$A = (3.2)$ $A=(3.2)$

$B = (6, 8)$ $B=(6,8)$

Let $A'B'$ be the line segment after the dilatation $X4$

The center of dilatation is $D=(1,3)$

$vec(DA')=4vec(DA)=4*<2,-1> = <8,-4>$

$A'=(8+1,-4+3)=(9,-1)$

$vec(DB')=4vec(DB)=4*<5,5> = <20,20>$

$B'=(20+1,20+3)=(21,23)$

The length of the line segment

$A'B'=sqrt((21-9)^2+(23+1)^2)$

$=sqrt(12^2+24^2)=26.8$

A line segment has endpoints at (3 ,2 )(3,2)(3 ,2 ) and (6 ,8 )(6,8)(6 ,8 ). The line segment is dilated by a factor of 4 44 around (1 ,3 )(1,3)(1 ,3 ). What are the new endpoints and length of the line segment?