A line segment has endpoints at (3 ,2 )(3,2) and (5 ,4 )(5,4). The line segment is dilated by a factor of 4 4 around (1 ,3 )(1,3). What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

color(brown)("New coordinates are " (9, -1), (17, 7)New coordinates are (9,−1),(17,7)

color(brown)("Length of the line segment '" = sqrt((9-17)^2 + (-1-7)^2) ~~ 11.3137Length of the line segment '=√(9−17)2+(−1−7)2≈11.3137

Explanation:

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

A'((x),(y)) =(4)a - (3)d =(4)*((3),(2)) - (3)*((1),(3)) = ((9),(-1))

B'((x),(y)) = (4)b - (3)d = (4)*((5),(4)) - (3)*((1),(3)) = ((17),(7))

color(brown)("New coordinates are " (9, -1), (17, 7)

color(brown)("Length of the line segment '" = sqrt((9-17)^2 + (-1-7)^2) ~~ 11.3137

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