A line segment has endpoints at $(7 ,4 )$ and $(3 ,8 )$ . The line segment is dilated by a factor of $5$ around $(4 ,2 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T04:39:23

$color(magenta)("New end points are " (19,12), (-1,32)$

$color(magenta)("Length of the line segment '" = sqrt((19- -1)^2 + (12-32)^2) = 20 sqrt2~~ 28.2843$

$A(7,4), B(3,8), " about point " D (4,2), " dilation factor "5$

$A'((x),(y)) =(5)a - (4)d =(5)*((7),(4)) - (4)*((4),(2)) = ((19),(12))$

$B'((x),(y)) = (5)b - (4)d = (5)*((3),(8)) - (4)*((4),(2)) = ((-1),(32)$

$color(magenta)("New end points are " (19,12), (-1,32)$

$color(magenta)("Length of the line segment '" = sqrt((19- -1)^2 + (12-32)^2) = 20 sqrt2~~ 28.2843$

A line segment has endpoints at (7 ,4 )(7 ,4 ) and (3 ,8 )(3 ,8 ). The line segment is dilated by a factor of 5 5 around (4 ,2 )(4 ,2 ). What are the new endpoints and length of the line segment?