A line segment has endpoints at $(3 ,2 )$ and $(5 ,4 )$ . The line segment is dilated by a factor of $4$ around $(1 ,3 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T02:57:09

$color(brown)("New coordinates are " (9, -1), (17, 7)$

$color(brown)("Length of the line segment '" = sqrt((9-17)^2 + (-1-7)^2) ~~ 11.3137$

$A(8,4), B(3,2), " about point " D (1,3), " dilation factor "4$

$A'((x),(y)) =(4)a - (3)d =(4)*((3),(2)) - (3)*((1),(3)) = ((9),(-1))$

$B'((x),(y)) = (4)b - (3)d = (4)*((5),(4)) - (3)*((1),(3)) = ((17),(7))$

$color(brown)("New coordinates are " (9, -1), (17, 7)$

$color(brown)("Length of the line segment '" = sqrt((9-17)^2 + (-1-7)^2) ~~ 11.3137$

A line segment has endpoints at (3 ,2 )(3 ,2 ) and (5 ,4 )(5 ,4 ). The line segment is dilated by a factor of 4 4 around (1 ,3 )(1 ,3 ). What are the new endpoints and length of the line segment?