A line segment has endpoints at $(5 ,8 )$ and $(2 , 1)$ . The line segment is dilated by a factor of $1/2$ around $(3 , 5)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T04:57:15

$color(brown)("New end points are " (4,13/2), (5/2, 3)$

$color(brown)("Length of the line segment '" = sqrt((4- 5/2)^2 + (13/2-3)^2) ~~ 3.8079$

$A(5,8), B(2,1), " about point " D (3,5), " dilation factor " 1/2$

$A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((5),(8)) - (-1/2)*((3),(5)) = ((4),(13/2))$

$B'((x),(y)) = (1/2)b - (-1/2)d = (1/2)* ((2),(1)) - (-1/2)*((3),(5)) = ((5/2),(3)$

$color(brown)("New end points are " (4,13/2), (5/2, 3)$

$color(brown)("Length of the line segment '" = sqrt((4- 5/2)^2 + (13/2-3)^2) ~~ 3.8079$

A line segment has endpoints at (5 ,8 )(5 ,8 ) and (2 , 1)(2 , 1). The line segment is dilated by a factor of 1/2 1/2 around (3 , 5)(3 , 5). What are the new endpoints and length of the line segment?