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

1 Answer
Jul 14, 2018

#color(chocolate)("New coordinates are " (18,8), (3,17)#

#color(chocolate)("Length of the line segment " ~~ 17.4929#

Explanation:

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

#A'((x),(y)) =(3)a - (2)d =(3)*((8),(4)) - (2)*((3),(2)) = ((18),(8))#

#B'((x),(y)) = (3)b - (2)d = (3)*((3),(7)) - (2)*((3),(2)) = ((3),(17))#

#color(chocolate)("New coordinates are " (18,8), (3,17)#

#color(chocolate)("Length of the line segment '" = sqrt((18-3)^2 + (8-17)^2) ~~ 17.4929#