A line segment has endpoints at $(5, 8)$ $(5 ,8 )$ and $(2, 1)$ $(2 , 1)$ . The line segment is dilated by a factor of $3$ $3$ around $(6, 4)$ $(6 , 4)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-26T03:09:12

$New coordinates are (3, 16), (- 6, - 5)$ $color(orange)("New coordinates are " (3,16), (-6, -5)$

$color(brown)("Length of the line segment after dilation " vec(A’B’) ~~ 22.8473$

$A(5, 8), B(2, 1), C(6, 4)$ , dilation factor $3$

$A’ = 3a - 2c$

$A’((x),(y)) = 3 * ((5),(8)) - 2 * ((6),(4))$

$A’((x),(y)) = ((3),(16))$

$B’((x),(y)) = 3 * ((2),(1)) - 2 * ((6),(4))$

$B’((x),(y)) = ((-6),(-5))$

$color(brown)("Length of the line segment after dilation "$

$color(green)(vec(A’B’) = sqrt((3- -6)^2 + (16- -5)^2) ~~ 22.8473$

A line segment has endpoints at (5 ,8 )(5,8)(5 ,8 ) and (2 , 1)(2,1)(2 , 1). The line segment is dilated by a factor of 3 33 around (6 , 4)(6,4)(6 , 4). What are the new endpoints and length of the line segment?