A line segment has endpoints at $(0 ,9 )$ and $(8 ,2 )$ . The line segment is dilated by a factor of $2$ around $(1 ,1 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-12T11:31:15

New end points $color(purple)(((-1),(17)),((15),(3))$

Length of the line segment $~~ color(green)(21.26)$

$A ((0),(9)), B ((8),(2)), C ((1),(1))$ Dilation factor around C is 2

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

$a' = 2 ((0),(9)) - ((1),(1)) = ((-1),(17))$

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

$b' = 2((8),(2)) - ((1),(1)) = ((15),(3))$

$vec(A'B') = sqrt((15+1)^2 + (3-17)^2) ~~ color(green)(21.26)$

A line segment has endpoints at (0 ,9 )(0 ,9 ) and (8 ,2 )(8 ,2 ). The line segment is dilated by a factor of 2 2 around (1 ,1 )(1 ,1 ). What are the new endpoints and length of the line segment?