A line segment has endpoints at #(7 ,4 )# and #(3 ,8 )#. The line segment is dilated by a factor of #5 # around #(4 ,2 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(magenta)("New end points are " (19,12), (-1,32)#

#color(magenta)("Length of the line segment '" = sqrt((19- -1)^2 + (12-32)^2) = 20 sqrt2~~ 28.2843#

Explanation:

#A(7,4), B(3,8), " about point " D (4,2), " dilation factor "5#

#A'((x),(y)) =(5)a - (4)d =(5)*((7),(4)) - (4)*((4),(2)) = ((19),(12))#

#B'((x),(y)) = (5)b - (4)d = (5)*((3),(8)) - (4)*((4),(2)) = ((-1),(32)#

#color(magenta)("New end points are " (19,12), (-1,32)#

#color(magenta)("Length of the line segment '" = sqrt((19- -1)^2 + (12-32)^2) = 20 sqrt2~~ 28.2843#

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