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

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Answer 1 · 2016-11-28T20:16:00

$"the new end points are:"A'(7,19),B'(-1,11)$

$"length of the new line segment is :"8sqrt 2$

$"1- draw Point objects A(4,7),B(2,5),D(3,3) and line segment"$

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$"2-find the new location of the Point B"$

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$x=3-1*4=3-4=-1$

$y=3+2*4=3+8=11$

$"the new location of B is "B'(-1,11)$

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$"3-find the new location of A"$

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$x=3+1*4=3+4=7$

$y=3+4*4=3+16=19$

$A'(7,19)$

$"4-draw the new line segment "A'(7,19),B'(-1,11)$

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$"length of the new line segment :"$

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$A'B'=sqrt((19-11)^2+(7+1)^2)$

$A'B'=sqrt(8^2+8^2)$

$A'B'=sqrt(64+64)$

$A'B'=8sqrt2$

A line segment has endpoints at (4 ,7 )(4,7)(4 ,7 ) and (2 ,5 )(2,5)(2 ,5 ). The line segment is dilated by a factor of 4 44 around (3 ,3 )(3,3)(3 ,3 ). What are the new endpoints and length of the line segment?