A line segment has endpoints at $(7, 6)$ $(7 ,6 )$ and $(5, 8)$ $(5 ,8 )$ . The line segment is dilated by a factor of $3$ $3$ around $(2, 4)$ $(2 ,4 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-07T09:55:33

The new emd points are $(17, 10)$ $(17,10)$ and $(11, 16)$ $(11,16)$
The length of the line segment is $= 8.49$ $=8.49$

Let the end points be $A = (7, 6)$ $A=(7,6)$ and $B = (5, 8)$ $B=(5,8)$

and $C = (2, 4)$ $C=(2,4)$

Let $A'$ and $B'$ be the new end points

Then,

$vec(CA')=3vec(CA)$

$=3*<7-2,6-4> =3*<5,2> = <15,6>$

$A'=(15,6)+(2,4)=(17,10)$

Similarly,

$vec(CB')=3vec(CB)$

$=3*<5-2,8-4> =3*<3,4> = <9,12>$

$B'=(9,12)+(2,4)=(11,16)$

The length of the line segment is

$A'B'=sqrt((11-17)^2+(16-10)^2)$

$=sqrt((6)^2+(6)^2)$

$=sqrt72$

$=8.49$

The length of the old line segment is

$AB=sqrt((5-7)^2+(8-6)^2)$

$=sqrt(4+4)$

$=sqrt(8)$

$=2.83$

$A'B'=3*AB$

A line segment has endpoints at (7 ,6 )(7,6)(7 ,6 ) and (5 ,8 )(5,8)(5 ,8 ). The line segment is dilated by a factor of 3 33 around (2 ,4 )(2,4)(2 ,4 ). What are the new endpoints and length of the line segment?