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

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Answer 1 · 2018-04-12T08:24:33

#color(violet)("Distance of A & B from origin after reflection and dilation " 9, 12.04 " respy."#

#A (1,2), B (4,1)," reflected across " x = -3, y = 1#

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

#A'(x,y) = A(2h-x, 2k-y) = (-6-1, 4-2) = (-7,2)#

#B'(x,y) = B(2h-x, 2k-y) = (-6-4, 4-1) = (-10,3)#

Points A' & B' dilated about C(2,2) by a factor of 2.

#A'(x,y) -> A''(x,y) = A'(x,y) - C(x,y) = ((-7,2) - (2,2)) = (-9,0)#

#B'(x,y) -> B''(x,y) = B'(x,y) - C(x,y) = ((-10,3) - (2,2)) = (-12,1)#

#OA' = 9, OB' = sqrt(-12^2 + 1^2 = 12.04#