A line segment has endpoints at (7 ,4 )(7,4) and (3 ,8 )(3,8). The line segment is dilated by a factor of 5 5 around (4 ,2 )(4,2). What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

color(magenta)("New end points are " (19,12), (-1,32)New end points are (19,12),(−1,32)

color(magenta)("Length of the line segment '" = sqrt((19- -1)^2 + (12-32)^2) = 20 sqrt2~~ 28.2843Length of the line segment '=√(19−−1)2+(12−32)2=20√2≈28.2843

Explanation:

A(7,4), B(3,8), " about point " D (4,2), " dilation factor "5A(7,4),B(3,8), about point D(4,2), dilation factor 5

A'((x),(y)) =(5)a - (4)d =(5)*((7),(4)) - (4)*((4),(2)) = ((19),(12))

B'((x),(y)) = (5)b - (4)d = (5)*((3),(8)) - (4)*((4),(2)) = ((-1),(32)

color(magenta)("New end points are " (19,12), (-1,32)

color(magenta)("Length of the line segment '" = sqrt((19- -1)^2 + (12-32)^2) = 20 sqrt2~~ 28.2843

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