Key Concepts: Transformations in the Coordinate Plane ⭐

Coordinate Proofs with Transformations

Use coordinate rules to verify transformation properties algebraically.

Summary of Coordinate Rules

• Translation by ⟨a, b⟩: (x, y) → (x + a, y + b)
• Reflection over x-axis: (x, y) → (x, −y)
• Reflection over y-axis: (x, y) → (−x, y)
• Rotation 90° CCW: (x, y) → (−y, x)
• Rotation 180°: (x, y) → (−x, −y)
• Dilation by factor k: (x, y) → (kx, ky)

Composing Transformations Algebraically

Apply each rule in sequence. For example, a rotation of 90° CCW followed by a reflection over the x-axis: (x, y) → (−y, x) → (−y, −x).

Identifying Transformations from Coordinates

Compare pre-image and image coordinates to determine which transformation was applied.