A line segment has endpoints at #(3 ,2 )# and #(5 ,4 )#. The line segment is dilated by a factor of #4 # around #(1 ,3 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(brown)("New coordinates are " (9, -1), (17, 7)#

#color(brown)("Length of the line segment '" = sqrt((9-17)^2 + (-1-7)^2) ~~ 11.3137#

Explanation:

#A(8,4), B(3,2), " about point " D (1,3), " dilation factor "4#

#A'((x),(y)) =(4)a - (3)d =(4)*((3),(2)) - (3)*((1),(3)) = ((9),(-1))#

#B'((x),(y)) = (4)b - (3)d = (4)*((5),(4)) - (3)*((1),(3)) = ((17),(7)) #

#color(brown)("New coordinates are " (9, -1), (17, 7)#

#color(brown)("Length of the line segment '" = sqrt((9-17)^2 + (-1-7)^2) ~~ 11.3137#

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