Reflection — Important Questions

(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)

(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.

(0, -3)

Point (0, -3) lies on the y-axis. When reflecting across the y-axis, points on the y-axis are invariant (don't change). So (0, -3) remains (0, -3).