A line segment has endpoints at $(1 ,4 )$ and $(7 ,3 )$ . The line segment is dilated by a factor of $3$ around $(2 ,6 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-20T08:38:04

New end points $A’((-1),(0))$ , $B’((17),(-3))$

Length of line segment after dilation

$vec(A’B’) = 16.2788$

$A (1,4), B (7,3)$ , dilated around $C (2,6)$ and dilation factor 3

$A’ = 3A - 2C = 3((1),(4)) - 2((2),(6)) = ((3),(12)) - ((4),(12)) = ((-1),(0))$

$B’ = 3B - 2C = 3((7),(3)) - 2((2),(6)) = ((21),(9)) - ((4),(12)) = ((17),(-3))$

Length of line segment after dilation

$vec(A’B’) = sqrt((17+1)^2 + (-3-0)^2) = 16.2788$

A line segment has endpoints at (1 ,4 )(1 ,4 ) and (7 ,3 )(7 ,3 ). The line segment is dilated by a factor of 3 3 around (2 ,6 )(2 ,6 ). What are the new endpoints and length of the line segment?