Key Concepts: Translations

Definition

A translation slides every point of a figure the same distance in the same direction. It is described by a vector ⟨a, b⟩.

Coordinate Rule

(x, y) → (x + a, y + b)

Properties of Translations

• A translation is an isometry (preserves distances and angle measures).
• All points move the same distance and direction.
• Orientation is preserved.
• Translated figures are congruent to the original.

Vectors

A translation vector ⟨a, b⟩ indicates a horizontal shift of a units and a vertical shift of b units.