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

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Answer 1 · 2018-06-08T01:36:36

$color(maroon)("New endpoints are" A' (5,21), B' (-4,0)$

$color(blue)("Length of the line segment "bar(A'B') = 15,23$

$A (5,9), B (2,2), C (5,3), " dilation factor " 2$

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

$A'((x),(y)) = 2((5),(9)) - ((5),(3)) = ((5),(15))$

$B'C = 2 (b - c)$ , $B' - c = 2(b - c)$ or $A' = 2b - c$

$B'((x),(y)) = 2((2),(2)) - ((5),(3)) = ((-1),(1))$

Length of the line segment

$bar(A'B') = sqrt((5+1)^2 + 14^2) = 15.23$

A line segment has endpoints at (5 ,9 )(5,9)(5 ,9 ) and (2 ,2 )(2,2)(2 ,2 ). The line segment is dilated by a factor of 2 22 around (5 ,3 )(5,3)(5 ,3 ). What are the new endpoints and length of the line segment?