A line segment has endpoints at #(75 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #2 # around #(4 , 5)#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(crimson)("New coordinates are " (146,11), (0, -3)#

#color(crimson)("Length of the line segment '" = sqrt((146-0)^2 + (11--3)^2) ~~ 146.6697#

Explanation:

#A(75,8), B(2,1)," about point " D (4,5), " dilation factor "2#

#A'((x),(y)) =(2)a - (1)d =(2)*((75),(8)) - (1)*((4),(5)) = ((146),(11))#

#B'((x),(y)) = (2)b - (1)d = (2)*((2),(1)) - (1)*((4),(5)) = ((0),(-3))#

#color(crimson)("New coordinates are " (146,11), (0, -3)#

#color(crimson)("Length of the line segment '" = sqrt((146-0)^2 + (11--3)^2) ~~ 146.6697#

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