A line segment has endpoints at $(5 ,9 )$ and $(8 ,2 )$ . The line segment is dilated by a factor of $2$ around $(5 ,3 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-17T02:13:11

$color(cyan)("New end points are " (5,15), (11,1)$

$color(cyan)("Length of the line segment '" ~~ 15.2315$

$A(5,9), B(8,2), " about point " D (5,3), " dilation factor " 2$

$A'((x),(y)) =(2)a - (1)d =(2)* ((5),(9)) - (1)*((5),(3)) = ((5),(15))$

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

$color(cyan)("New end points are " (5,15), (11,1)$

$color(cyan)("Length of the line segment '" = sqrt((5-11)^2 + (15-1)^2) ~~ 15.2315$

A line segment has endpoints at (5 ,9 )(5 ,9 ) and (8 ,2 )(8 ,2 ). The line segment is dilated by a factor of 2 2 around (5 ,3 )(5 ,3 ). What are the new endpoints and length of the line segment?