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

Question

1522 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-08T11:49:20

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

$color(indigo)(vec(A'B') = 14.42 " units"$

$A(4,3), B(2,6), " dilated by a factor of 4 about " C(3,3)$

$A'((x),(y)) = 4a - 3c = 4 ((4),(3)) - 3 ((3),(3)) = ((7),(3))$

$B'((x),(y)) = 4b - 3c = 4 ((2),(6)) - 3 ((3),(3)) = ((-1),(15))$

$color(brown)(vec(A'B') = sqrt((-1-7)^2 + (15-3)^2) = 14.42 " units"$

A line segment has endpoints at (4 ,3 )(4,3)(4 ,3 ) and (2 ,6 )(2,6)(2 ,6 ). The line segment is dilated by a factor of 4 44 around (3 ,3 )(3,3)(3 ,3 ). What are the new endpoints and length of the line segment?