Geometry Reflection, Translation & Rotation Formulas

Reflection Formulas

• Reflection in the x-axis: Changes the y-coordinate's sign while keeping the x-coordinate the same, represented as (x, y) -> (x, -y).
• Reflection in the y-axis: Changes the x-coordinate's sign while retaining the y-coordinate, detailed as (x, y) -> (-x, y).
• Reflection in the line y = x: Swaps the x and y coordinates, noted as (x, y) -> (y, x).
• Reflection in the line y = -x: Swaps and negates both coordinates, expressed as (x, y) -> (-y, -x).

Translation Formula

• Translation on a coordinate plane: Moves a point horizontally and vertically by adding specific values to the coordinates, formulated as (x, y) -> (x + a, y + b).

Rotation Formulas

• 90-degree rotation: Converts coordinate (x, y) to (-y, x), effectively rotating the point counterclockwise.
• 180-degree rotation: Rotates points to the opposite direction in a straightforward manner, shown as (x, y) -> (-x, -y).
• 270-degree rotation: Turns points clockwise to (-y, x), altering their positions in the plane accordingly.