A line segment has endpoints at $(5 ,1 )$ and $(3 ,9 )$ . The line segment is dilated by a factor of $5$ around $(2 ,2 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-05T11:33:25

New end points $A' color(brown)( ((17,-3)),$ $B' color(brown)((7,37)$

Length of the line segment $vec(A'B') ~~ color(green)(41.23$

Given : A(5,1), B(3,9), dilated around C (2,2) & dilation factor 5

To find : End points and length of line segment after dilation

$vec(A'C) = 5 * vec(AC)$ or $a' = 5a - 4c$

$a' = 5((5),(1)) - 4((2),(2)) = ((25),(5)) - ((8),(8)) =color(brown)( ((17),(-3))$

$vec(B'C) = 5 * vec(BC)$ or $b' = 5b - 4c$

$b' = 5((3),(9)) - 4((2),(2)) = ((15),(45)) - ((8),(8)) = color(brown)( ((7),(37))$

$vec(A'B') = sqrt((17-7)^2 + (-3 -37)^2) ~~ color(green)(41.23$

A line segment has endpoints at (5 ,1 )(5 ,1 ) and (3 ,9 )(3 ,9 ). The line segment is dilated by a factor of 5 5 around (2 ,2 )(2 ,2 ). What are the new endpoints and length of the line segment?