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

1 Answer
sankarankalyanam
Jul 14, 2018

color(purple)("New coordinates are " (7, 3), (-1, 11)New coordinates are (7,3),(−1,11)

color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137Length of the line segment '=√(7−−1)2+(3−11)2≈11.3137

Explanation:

A(8,4), B(4,3), " about point " D (1,3), " dilation factor "4A(8,4),B(4,3), about point D(1,3), dilation factor 4

A'((x),(y)) =(4)a - (3)d =(4)*((4),(3)) - (3)*((3),(3)) = ((7),(3))

B'((x),(y)) = (4)b - (3)d = (4)*((2),(5)) - (3)*((3),(3)) = ((-1),(11))

color(purple)("New coordinates are " (7, 3), (-1, 11)

color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137

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