#A(1,1), B(4,2) " reflected across " x = 2, y = -1 " in that order"#
#"Reflection rule : reflect thru " x = 2, y = -1, h=2, k= -1. (2h-x, 2k-y)#
#A'(x,y) = (2h-x, 2k-y) = (4-1, -2-1) = (3, -3)#
#B'(x,y) = (2h-x, 2k-y) = (4-4, -2-2) = (0, -4)#
#"A', B' dilated about C (1,1) by a factor of 2"#
#A'(x,y) -> A''(x,y) = 2*A'(x,) - C(x,y) = ((6,-6)-(1,1)) = (5,-7)#
#B'(x,y) -> B''(x,y) = 2*B'(x,y) - C(x,y) = ((0,-8)-(1,1)) = (-1,-9)#
#OA'' = sqrt(5^2 + 7^2) = 8.6#
#OB'' = sqrt(15^2 + 9^2) = 9.06#
#color(purple)("Distance of A from origin after reflection and dilation " = 8.6#
#color(purple)("Distance of B from origin after reflection and dilation " = 9.06#