A line segment goes from #(2 ,3 )# to #(4 ,1 )#. The line segment is dilated about #(0 ,1 )# by a factor of #3#. Then the line segment is reflected across the lines #x=2# and #y=-1#, in that order. How far are the new endpoints from the origin?

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Answer 1 · 2018-08-07T02:17:58

#color(purple)("Distances of A & B after dilation and reflection "#

#color(green)(sqrt 85, sqrt73 " respectivelyy."#

#A (2, 3), B (4,1), " dilated by factor 3 about " C(0,1)#

#A(x,y) -> A'(x,y) = 3* A(x,y) - 2*C(x,y) = (3*(2,3) - 2*(0,1)) = (6,7)#

#B(x,y) -> B'(x,y) = 3* B(x,y) - 2*C(x,y) = (3*(4,1) - 2*(0,1)) = (12,1)#

#"Reflection Rule : reflect thru " x = 2, y = -1; h=2, k= -1; (2h-x, 2k-y)#

#A''(x,y) = A'((2h - x), (2k - y)) = (4-6, -2-7) = (-2, -9)#

#B''(x,y) = B'((2h - x), (2k - y)) = (4-12, -2-1) = (-8, -3)#

#OA'' = sqrt(-2^2 + -9^2) = sqrt85#

#OB'' = sqrt(-8^2 + -3^2) = sqrt 73#