ICSE Class 10 Maths: Reflection — Coordinate Geometry Notes 2026

Reflection in the X-Axis

• Rule: P(x, y) → P'(x, −y); x-coordinate unchanged, y-coordinate changes sign
• Example: A(3, 4) reflected in x-axis gives A'(3, −4)
• Application: 'find image' questions common in ICSE; always mark original and image points

Reflection in the Y-Axis

• Rule: P(x, y) → P'(−x, y); y-coordinate unchanged, x-coordinate changes sign
• Example: B(−2, 5) reflected in y-axis gives B'(2, 5)
• Key distinction: x-axis reflection changes y; y-axis reflection changes x

Reflection in the Origin

• Rule: P(x, y) → P'(−x, −y); both coordinates change sign
• Equivalent to 180° rotation about origin
• Example: C(4, −3) reflected in origin gives C'(−4, 3)

Reflection in the Line y = x

• Rule: P(x, y) → P'(y, x); coordinates are swapped
• Example: D(2, 7) → D'(7, 2)
• Line y = x is perpendicular bisector of the line segment DD'

Reflection in the Line y = −x

• Rule: P(x, y) → P'(−y, −x); coordinates are swapped and both signs changed
• Example: E(3, −1) → E'(1, −3)
• Rarely tested in ICSE but important to distinguish from y = x reflection

Invariant Points

• A point is invariant under reflection if it lies on the mirror line
• Reflection in x-axis: all points on x-axis (y = 0) are invariant
• Reflection in y = x: all points where x = y are invariant (e.g., (3,3), (−2,−2))

ICSE Exam Tips

• Questions often combine reflection with coordinates of quadrilateral vertices
• Always show the line of reflection as dotted in diagrams
• Multi-step question: reflect P in x-axis to get P', then reflect P' in y = x to get P'' — track each step