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

1 Answer
sankarankalyanam
Jul 14, 2018

color(violet)("New end points are " (3/2, 7/2), (5/2,3)New end points are (32,72),(52,3)

color(violet)("Length of the line segment '" = sqrt((3/2- 5/2)^2 + (7/2-3)^2) ~~ 1.118Length of the line segment '=√(32−52)2+(72−3)2≈1.118

Explanation:

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

A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((1),(2)) - (-1/2)*((2),(5)) = ((3/2),(7/2))

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

color(violet)("New end points are " (3/2, 7/2), (5/2,3)

color(violet)("Length of the line segment '" = sqrt((3/2- 5/2)^2 + (7/2-3)^2) ~~ 1.118

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