A line segment has endpoints at $(3, 8)$ $(3 ,8 )$ and $(3, 9)$ $(3 , 9)$ . The line segment is dilated by a factor of $3$ $3$ around $(2, 3)$ $(2 , 3)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-07T13:58:44

New end points are $(5, 18) & (5, 21)$ $(5,18) & (5,21)$

Length of the line segment after dilation is $3$ $3$

$A (3, 8), B (3, 9), C (2, 3)$ $A(3,8), B(3,9), C(2,3)$ , dilation factor $3$ $3$

$A’ = 3a - 2c$

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

$A’((x),(y)) = ((5),(18))$

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

$B’((x),(y)) = ((5),(21))$

Length of the line segment after dilation

$vec(A’B’) = sqrt((5-5)^2 + (21-18)^2) = 3$

A line segment has endpoints at (3 ,8 )(3,8)(3 ,8 ) and (3 , 9)(3,9)(3 , 9). The line segment is dilated by a factor of 3 33 around (2 , 3)(2,3)(2 , 3). What are the new endpoints and length of the line segment?