A line segment has endpoints at $(2 ,7 )$ and $(5 ,4 )$ . The line segment is dilated by a factor of $2$ around $(4 ,3 )$ . What are the new endpoints and length of the line segment?

Question

1815 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-10T08:45:00

$color(violet)("New end points are " (0,110, (6,5) " and the length of the line segment is " 8.49$

$A(2,7), B(5,4), " about "C(4,3) " & dilated by factor " 2$

$A'((x),(y)) = 2a -c = 2 * ((2),(7)) - ((4),(3)) = ((0), (11))$

$B'((x),(y)) = 2b -c = 2 * ((5),(4)) - ((4),(3)) = ((6), (5))$

$"Length of the line segment after dilation " = vec(A'B')$

$vec (A'B') = sqrt((0-6)^2 = (11-5)^2) = 8.49$

A line segment has endpoints at (2 ,7 )(2 ,7 ) and (5 ,4 )(5 ,4 ). The line segment is dilated by a factor of 2 2 around (4 ,3 )(4 ,3 ). What are the new endpoints and length of the line segment?