A line segment has endpoints at $(7 ,6 )$ and $(9 ,2 )$ . The line segment is dilated by a factor of $4$ around $(4 ,3 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2016-11-16T13:30:38

$"please have a look the animation below"$

$"The new end points of line segment are :"F(16,15),I(24,-1)$

$"Length of the line segment is :"17.89$

enter image source here

$"the coordinates of point F:"$

$CJ*"factor"=3*4=12$

$4+12=16" the x coordinate of F"$

$AJ*"factor"=3*4=12$

$3+12=15"the y coordinate of F"$

$F(16,15)$

$"the coordinates of I Point:"$

$ZB*"factor"=5*4=20$

$4+20=24" the x coordinate of I"$

$CZ*"factor"=1*4=4$

$3-4=-1" the y coordinate of I")$

$I=(24,-1)$

$"the length of line segment FI :"$

FI=sqrt((16-24)^2+(15+1)^2)

$FI=sqrt(64+256)$

$FI=sqrt(320)$

$FI=17.89$

A line segment has endpoints at (7 ,6 )(7 ,6 ) and (9 ,2 )(9 ,2 ). The line segment is dilated by a factor of 4 4 around (4 ,3 )(4 ,3 ). What are the new endpoints and length of the line segment?