A line segment has endpoints at $(5 ,6 )$ and $(7 , 3)$ . The line segment is dilated by a factor of $2$ around $(4 , 2)$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-14T05:01:48

$color(indigo)("New end points are " (6,10), (0,0)$

$color(indigo)("Length of the line segment '" = sqrt((6)^2 + (10)^2) ~~ 11.6619$

$A(5,6), B(7,3), " about point " D (4,2), " dilation factor " 2$

$A'((x),(y)) =(2)a - (1)d =(2)* ((5),(6)) - (1)*((4),(2)) = ((6),(10))$

$B'((x),(y)) = (2)b - (1)d = (2)* ((2),(1)) - (1)*((4),(2)) = ((0),(0)$

$color(indigo)("New end points are " (6,10), (0,0)$

$color(indigo)("Length of the line segment '" = sqrt((6)^2 + (10)^2) ~~ 11.6619$

A line segment has endpoints at (5 ,6 )(5 ,6 ) and (7 , 3)(7 , 3). The line segment is dilated by a factor of 2 2 around (4 , 2)(4 , 2). What are the new endpoints and length of the line segment?