A line segment goes from #(2 ,3 )# to #(4 ,1 )#. The line segment is dilated about #(1 ,1 )# by a factor of #2#. 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 · 2018-04-12T04:18:25

#"Distance of the two points from origin after dilation and reflection "#
#color(blue)( 3.16, 4.24)#

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

#A'(x,) = 2 * A(x,y) - C(x,y) =( (4,6) - (1,1)) = (3,5)#

#B'(x,) = 2 * B(x,y) - C(x,y) =( (8,2) - (1,1)) = (7,1)#

#color(crimson)("reflect thru across " x=2, y = -1, h=2 k= -1. (2h-x, 2k-y)"#

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

#B''(x,y) = (2 * 2 - 7), (2*-1 - 1) = (-3, -3)#

#A''O = sqrt(1^2 + 3^3) = 3.16#

#B''O = sqrt(3^2 + 3^2) = 4.24#