A line segment has endpoints at (75 ,8 )(75,8) and (2 , 1)(2,1). The line segment is dilated by a factor of 2 2 around (4 , 5)(4,5). What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

color(crimson)("New coordinates are " (146,11), (0, -3)New coordinates are (146,11),(0,−3)

color(crimson)("Length of the line segment '" = sqrt((146-0)^2 + (11--3)^2) ~~ 146.6697Length of the line segment '=√(146−0)2+(11−−3)2≈146.6697

Explanation:

A(75,8), B(2,1)," about point " D (4,5), " dilation factor "2A(75,8),B(2,1), about point D(4,5), dilation factor 2

A'((x),(y)) =(2)a - (1)d =(2)*((75),(8)) - (1)*((4),(5)) = ((146),(11))

B'((x),(y)) = (2)b - (1)d = (2)*((2),(1)) - (1)*((4),(5)) = ((0),(-3))

color(crimson)("New coordinates are " (146,11), (0, -3)

color(crimson)("Length of the line segment '" = sqrt((146-0)^2 + (11--3)^2) ~~ 146.6697

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