A line segment has endpoints at $(9, 3)$ $(9 ,3 )$ and $(5, 9)$ $(5 ,9 )$ . The line segment is dilated by a factor of $3$ $3$ around $(4, 4)$ $(4 ,4 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-27T05:52:43

$color(brown)(A' (19,1), B' (7,18)$

$color(chocolate)("Length of the line segment after dilation "color(blue)(vec(A’B’) ~~ 21.6333$

$A(9, 3), B(5, 9), C(64, 4)$ , dilation factor $3$

$A’ = 3a - 2c$

$A’((x),(y)) = 3 * ((9),(3)) - 2 * ((4),(4))$

$A’((x),(y)) = ((19),(1))$

$B’((x),(y)) = 3 * ((5),(9)) - 2 * ((4),(4))$

$B’((x),(y)) = ((7),(19))$

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

$color(blue)(vec(A’B’) = sqrt((19- 7)^2 + (1- 19)^2) ~~ 21.6333$

A line segment has endpoints at (9 ,3 )(9,3)(9 ,3 ) and (5 ,9 )(5,9)(5 ,9 ). The line segment is dilated by a factor of 3 33 around (4 ,4 )(4,4)(4 ,4 ). What are the new endpoints and length of the line segment?