A line segment has endpoints at $(1 ,2 )$ and $(3 , 9)$ . The line segment is dilated by a factor of $1/2$ around $(4 , 2)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T04:49:44

$color(red)("New end points are " (5/2, 2), (7/2,11/2)$

$color(red)("Length of the line segment '" = sqrt((5/2- 7/2)^2 + (11/2-2)^2) ~~ 3.64$

$A(1,2), B(3,9), " about point " D (4,2), " dilation factor " 1/2$

$A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((1),(2)) - (-1/2)*((4),(2)) = ((5/2),(2))$

$B'((x),(y)) = (1/2)b - (-1/2)d = (1/2)* ((3),(9)) - (-1/2)*((4),(2)) = ((7/2),(11/2)$

$color(red)("New end points are " (5/2, 2), (7/2,11/2)$

$color(red)("Length of the line segment '" = sqrt((5/2- 7/2)^2 + (11/2-2)^2) ~~ 3.64$

A line segment has endpoints at (1 ,2 )(1 ,2 ) and (3 , 9)(3 , 9). The line segment is dilated by a factor of 1/2 1/2 around (4 , 2)(4 , 2). What are the new endpoints and length of the line segment?