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

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Answer 1 · 2018-04-12T08:09:39

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

#color(green)(9.4868, 1.4142 " respy."#

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

#A(x,y) -> A'(x,y) = 2* A(x,y) - C(x,y) = (2*(3,2) - (1,1)) = (5,3)#

#B(x,y) -> B'(x,y) = 2* B(x,y) - C(x,y) = (2*(1,3) - (1,1)) = (1,5)#

#"Reflection Rule : reflect thru " x = 1, y = -3; h=1, k= -3; (2h-x, 2k-y)#

#A''(x,y) = A'((2h - x), (2k - y)) = (2-5, -6-3) = (-3, -9)#

#B''(x,y) = B'((2h - x), (2k - y)) = (2-1, -6+5) = (1, -1)#

#OA'' = sqrt(-3^2 + -9^2) = 9.4868#

#OB'' = sqrt(1^2 + -1^2) = 1.4142#