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

1 Answer
sankarankalyanam
Jul 14, 2018

#color(purple)("New end points are " (15,1), (9,18)#

#color(crimson)("Length of the line segment " ~~ 18.0278#

Explanation:

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

#A'((x),(y)) =(3)a - (2)d =(3)* ((7),(3)) - (2)*((3),(4)) = ((15),(1))#

#B'((x),(y)) = (3)b - (2)d = (3)* ((5),(8)) - (2)*((3),(4)) = ((9),(18)#

#color(purple)("New end points are " (15,1), (9,18)#

#color(crimson)("Length of the line segment " = sqrt((15-9)^2 + (1-18)^2) ~~ 18.0278#

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