A line segment has endpoints at (8 ,4 )(8,4) and (3 ,7 )(3,7). The line segment is dilated by a factor of 1/2 12 around (3 ,2 )(3,2). What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

color(purple)("New end points are " (11/2, 3), (3,9/2)New end points are (112,3),(3,92)

color(purple)("Length of the line segment '" = sqrt((11/2- 3)^2 + (3-9/2)^2) ~~ 2.9155Length of the line segment '=√(112−3)2+(3−92)2≈2.9155

Explanation:

A(8,4), B(3,7), " about point " D (3,2), " dilation factor " 1/2A(8,4),B(3,7), about point D(3,2), dilation factor 12

A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((8),(4)) - (-1/2)*((3),(2)) = ((11/2),(3))

B'((x),(y)) = (1/2)b - (-1/2)d = (1/2)* ((3),(7)) - (-1/2)*((3),(2)) = ((7/2),(11/2)

color(purple)("New end points are " (11/2, 3), (3,9/2)

color(purple)("Length of the line segment '" = sqrt((11/2- 3)^2 + (3-9/2)^2) ~~ 2.9155

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