A line segment has endpoints at $(8 ,4 )$ and $(3 ,7 )$ . The line segment is dilated by a factor of $3$ around $(3 ,2 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T02:52:29

$color(chocolate)("New coordinates are " (18,8), (3,17)$

$color(chocolate)("Length of the line segment " ~~ 17.4929$

$A(8,4), B(2,3), " about point " D (3,2), " dilation factor "3$

$A'((x),(y)) =(3)a - (2)d =(3)*((8),(4)) - (2)*((3),(2)) = ((18),(8))$

$B'((x),(y)) = (3)b - (2)d = (3)*((3),(7)) - (2)*((3),(2)) = ((3),(17))$

$color(chocolate)("New coordinates are " (18,8), (3,17)$

$color(chocolate)("Length of the line segment '" = sqrt((18-3)^2 + (8-17)^2) ~~ 17.4929$

A line segment has endpoints at (8 ,4 )(8 ,4 ) and (3 ,7 )(3 ,7 ). The line segment is dilated by a factor of 3 3 around (3 ,2 )(3 ,2 ). What are the new endpoints and length of the line segment?