Reflection

(0, 0), (5, 0), (-2, 0)

Invariant points on x-axis reflection are points that lie on the x-axis itself (y = 0). These points don't change when reflected. Points with y = 0 remain unchanged.

(5, 1)

For reflection in line x = a, use formula (x, y) → (-x + 2a, y). Here a = 1, so (-3, 1) → (-(-3) + 2×1, 1) = (3 + 2, 1) = (5, 1)

Reflection in origin, Reflection in line y = x

Reflection in origin changes both coordinates: (x, y) → (-x, -y). Reflection in line y = x swaps coordinates: (x, y) → (y, x). Other reflections change only one coordinate.

(2, 5)

Reflection in x-axis keeps x-coordinate same and changes sign of y-coordinate. So A(2, -5) → A'(2, 5). The y-coordinate changes from -5 to 5.