A line segment has endpoints at $(1 ,4 )$ and $(5 ,3 )$ . The line segment is dilated by a factor of $3$ around $(2 ,6 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-05T11:43:53

New end points $color(purple)(A' (-1,0)$ , $color(purple)(B' (11,-3)$

Length of the line segment after dilation is

$vec(A'B') ~~ color(green)(12.37)$ rounded to 2 decimals

Given : A(1,4), B(5,3), Dilated around C(2,6), dilation factor 3

To find the new end points and length of line segment.

$vec(A'C) = 3 * vec(AC)$ or $a' = 3a - 2c$

$a' = 3 ((1),(4)) - 2 ((2),(6)) = ((3),(12)) - ((4),(12)) = color(purple)(((-1),(0))$

$vec(B'C) = 3 * vec(BC)$ or $b' = 3b - 2c$

$b' = 3 ((5),(3)) - 2 ((2),(6)) = ((15),(9)) - ((4),(12)) = color(purple)(((11),(-3))$

$vec(A'B') = sqrt((-1-11)^2 + (0-(-3))^2) ~~ color(green)(12.37)$ rounded to 2 decimals

A line segment has endpoints at (1 ,4 )(1 ,4 ) and (5 ,3 )(5 ,3 ). The line segment is dilated by a factor of 3 3 around (2 ,6 )(2 ,6 ). What are the new endpoints and length of the line segment?