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

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Answer 1 · 2018-07-14T02:59:46

$color(purple)("New coordinates are " (7, 3), (-1, 11)$

$color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137$

$A(8,4), B(4,3), " about point " D (1,3), " dilation factor "4$

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

$B'((x),(y)) = (4)b - (3)d = (4)*((2),(5)) - (3)*((3),(3)) = ((-1),(11))$

$color(purple)("New coordinates are " (7, 3), (-1, 11)$

$color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137$

A line segment has endpoints at (4 ,3 )(4 ,3 ) and (2 ,5 )(2 ,5 ). 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?