A line segment has endpoints at $(3 ,5 )$ and $(6 ,1 )$ . The line segment is dilated by a factor of $4$ around $(6 ,2 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-20T08:10:02

New points $A’ ((-6),(14))$ , $B’ ((6),(-2))$

Length of the line segment after dilation $vec(A’B’) = 18.44$

$A (3, 5), B ( 6, 1)$ . Dilated around $C (6,2$ by factor 4.

$vec (A’C) = 4 * vec(AC)$

$A’ - c= 4 * (a - c)$

$A’ = 4a - 3c$

$A’((x),(y)) = 4 ((3),(5)) - 3((6),(2)) = ((12),(20)) - ((18),(6)) = ((-6),(14))$

$A’ ((-6),(14))$

Similarly,

$vec(B’C) = 4 vec(AB)$

$B’((x),(y)) = 4((6),(1)) - 3((6),(2)) = ((24),(4)) - ((18),(6)) = ((6),(-2))$

$B’ ((6),(-2))$

Using distance formula, $vec(AB) = sqrt((3-6)^2 + (5-1)^2) = 5$

$vec(A’B’) = sqrt((-6-6)^2 + (14+2)^2) ~~ 18.44$

A line segment has endpoints at (3 ,5 )(3 ,5 ) and (6 ,1 )(6 ,1 ). The line segment is dilated by a factor of 4 4 around (6 ,2 )(6 ,2 ). What are the new endpoints and length of the line segment?