The diagram above shows a triangle ABC in which A is (5,8), B is (2,4), C is (9,6). The point X is (2,2). Draw the images after the following transformations have been applied to triangle ABC

For $A(5, 8)$: $A' = (5, -8)$
For $B(2, 4)$: $B' = (2, -4)$
For $C(9, 6)$: $C' = (9, -6)$

The vertices of the reflected triangle $A'B'C'$ are $\boxed{\text{}A'(5, -8), B'(2, -4), C'(9, -6)\text{}}$

For $A(5, 8)$: $A'' = (5 + (-3), 8 + 7) = (2, 15)$
For $B(2, 4)$: $B'' = (2 + (-3), 4 + 7) = (-1, 11)$
For $C(9, 6)$: $C'' = (9 + (-3), 6 + 7) = (6, 13)$

The vertices of the translated triangle $A''B''C''$ are $\boxed{\text{}A''(2, 15), B''(-1, 11), C''(6, 13)\text{}}$

For $A(5, 8)$: $(5-2, 8-2) = (3, 6)$
For $B(2, 4)$: $(2-2, 4-2) = (0, 2)$
For $C(9, 6)$: $(9-2, 6-2) = (7, 4)$

For $(3, 6)$: $(6, -3)$
For $(0, 2)$: $(2, -0) = (2, 0)$
For $(7, 4)$: $(4, -7)$

For $(6, -3)$: $A''' = (6+2, -3+2) = (8, -1)$
For $(2, 0)$: $B''' = (2+2, 0+2) = (4, 2)$
For $(4, -7)$: $C''' = (4+2, -7+2) = (6, -5)$

The vertices of the rotated triangle $A'''B'''C'''$ are $\boxed{\text{}A'''(8, -1), B'''(4, 2), C'''(6, -5)\text{}}$