A line segment has endpoints at #(5 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #3 # around #(6 , 4)#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-26T03:09:12

#color(orange)("New coordinates are " (3,16), (-6, -5)#

#color(brown)("Length of the line segment after dilation " vec(A’B’) ~~ 22.8473#

#A(5, 8), B(2, 1), C(6, 4)#, dilation factor #3#

#A’ = 3a - 2c#

#A’((x),(y)) = 3 * ((5),(8)) - 2 * ((6),(4))#

#A’((x),(y)) = ((3),(16))#

#B’((x),(y)) = 3 * ((2),(1)) - 2 * ((6),(4))#

#B’((x),(y)) = ((-6),(-5))#

#color(brown)("Length of the line segment after dilation "#

#color(green)(vec(A’B’) = sqrt((3- -6)^2 + (16- -5)^2) ~~ 22.8473#