A line segment has endpoints at (5 ,8 )(5,8) and (2 , 1)(2,1). The line segment is dilated by a factor of 1/2 12 around (3 , 5)(3,5). What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

color(brown)("New end points are " (4,13/2), (5/2, 3)New end points are (4,132),(52,3)

color(brown)("Length of the line segment '" = sqrt((4- 5/2)^2 + (13/2-3)^2) ~~ 3.8079Length of the line segment '=√(4−52)2+(132−3)2≈3.8079

Explanation:

A(5,8), B(2,1), " about point " D (3,5), " dilation factor " 1/2A(5,8),B(2,1), about point D(3,5), dilation factor 12

A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((5),(8)) - (-1/2)*((3),(5)) = ((4),(13/2))

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

color(brown)("New end points are " (4,13/2), (5/2, 3)

color(brown)("Length of the line segment '" = sqrt((4- 5/2)^2 + (13/2-3)^2) ~~ 3.8079

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