A line segment has endpoints at #(3 ,6 )# and #(9 ,4 )#. The line segment is dilated by a factor of #4 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(crimson)("New end points are " (0,15), (24,7)#

#color(crimson)("Length of the line segment '" = sqrt((0-24)^2 + (15-7)^2) ~~ 25.2982#

Explanation:

#A(3,6), B(9,4), " about point " D (4,3), " dilation factor " 4#

#A'((x),(y)) =(4)a - (3)d =(4)* ((3),(6)) - (3)*((4),(3)) = ((0),(15))#

#B'((x),(y)) = (4)b - (3)d = (4)* ((9),(4)) - (3)*((4),(3)) = ((24),(7)#

#color(crimson)("New end points are " (0,15), (24,7)#

#color(crimson)("Length of the line segment '" = sqrt((0-24)^2 + (15-7)^2) ~~ 25.2982#

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