A line segment has endpoints at $(0 ,9 )$ and $(8 ,2 )$ . The line segment is dilated by a factor of $2$ around $(5 ,1 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T05:09:49

$color(blue)("New end points are " (-5,17), (11,3)$

$color(blue)("Length of the line segment '" = ~~ 22.0227$

$A(0,9), B(8,2), " about point " D (5,1), " dilation factor " 2$

$A'((x),(y)) =(2)a - (1)d =(2)* ((0),(9)) - (1)*((5),(1)) = ((-5),(17))$

$B'((x),(y)) = (2)b - (1)d = (2)* ((8),(2)) - (1)*((5),(1)) = ((11),(3)$

$color(blue)("New end points are " (-5,17), (11,3)$

$color(blue)("Length of the line segment '" = sqrt((-5-11)^2 + (17-3)^2) ~~ 22.0227$

A line segment has endpoints at (0 ,9 )(0 ,9 ) and (8 ,2 )(8 ,2 ). The line segment is dilated by a factor of 2 2 around (5 ,1 )(5 ,1 ). What are the new endpoints and length of the line segment?