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

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Answer 1 · 2018-07-14T05:22:07

$color(purple)("New end points are " (15,1), (9,18)$

$color(crimson)("Length of the line segment " ~~ 18.0278$

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

$A'((x),(y)) =(3)a - (2)d =(3)* ((7),(3)) - (2)*((3),(4)) = ((15),(1))$

$B'((x),(y)) = (3)b - (2)d = (3)* ((5),(8)) - (2)*((3),(4)) = ((9),(18)$

$color(purple)("New end points are " (15,1), (9,18)$

$color(crimson)("Length of the line segment " = sqrt((15-9)^2 + (1-18)^2) ~~ 18.0278$

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