Definition of Reflection:In coordinate geometry, reflection is a type of transformation that flips a point or a shape over a specific line, known as the mirror line. The image formed is a mirror image, and each point and its image are the same distance from the mirror line but on opposite sides.1. Reflection over the y-axis  (x = 0)Rule:If a point is P(x, y), then its reflection over the y-axis is:P(x, y)→  P'(-x, y)Explanation:The x-coordinate becomes negative (flipped), but the y-coordinate stays the same.Example:A(3,4)→ A'(-3, 4)2. Reflection over the x-axis  (y = 0)Rule:P(x, y)→  P'(x, -y)Explanation:The y-coordinate becomes negative (flipped), but the x-coordinate stays the same.Example:B(−5,2)→B'(-5, -2)3. Reflection over the line x = kRule:P(x, y)→P′(2k−x, P'(2k - x, y)Explanation:The distance from the line x = k is preserved, and the x-coordinate is mirrored about x=kx = k.Example: Reflect C(7,3) over the line x = 5:C(7,3)→ = C'(3, 3)4. Reflection over the line y=hy = hRule:P(x, y)→P P'(x, 2h - y)Explanation:The y-coordinate is flipped about the line y = h, while the x-coordinate remains unchanged.Example: Reflect D(−2,6)D(-2, 6) over the line y = 4:D(−2,6)→ D'(-2, 2)5. Reflection over the line y = xRule:P(x, y)→ P'(y, x)Explanation: The x and y coordinates are swapped.Example: E(2,7)→ E'(7, 2)6. Reflection over the line y = -xRule:P(x, y)→ P'(-y, -x)Explanation: The coordinates are swapped and negated.Example: F(3,−4)→F'(4, -3)Summary Table of Reflection RulesMirror LineRuleClassroom Activity Suggestion1. Plot any triangle △ABC on graph paper.Reflect it across different mirror lines: x=0x = 0, y=0y = 0, x = k, y = h, y=y = x, and y= -x.Label each reflected triangle A′B′C′.Verify that each pair of points and their reflections are equidistant from the mirror line.