A line segment goes from #(5 ,8 )# to #(4 ,2 )#. The line segment is reflected across #x=-3#, reflected across #y=-5#, and then dilated about #(2 ,0 )# by a factor of #2#. How far are the new endpoints from the origin?

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Answer 1 · 2017-06-05T22:53:56

#2 sqrt 202 and 4 sqrt 34#

#A_1 = (5, 8) ; B_1 = (4, 2)#

#-3 + x mapsto -3 - x#
#-3 + x+3 mapsto -3 - x - 3 = -6 -x#

#A_2 = (-6 -5, 8) ; B_2 = (-6 -4, 2)#

#-5 + y mapsto -5 - y#
#-5 + y + 5 mapsto -5 - y - 5 = -10 -y#

#A_3 = (-11, -10-8) ; B_3 = (-10, -10-2)#

What is to dilate the line about (2, 0) by a factor of 2?

I suppose #(x,y) mapsto (2x, y)#

#A_4 = (-11 * 2, -18) ; B_4 = (-10 * 2, -12)#

#|A_4|^2 = 22^2 + 18^2#

#|B_4|^2 = 20^2 + 12^2#