Translations on a coordinate plane

A horizontal translation adds or subtracts from the x-coordinate (e.g., move 3 right: x → x+3), and a vertical translation adds or subtracts from the y-coordinate (e.g., move 2 down: y → y−2) — the algebraic rule is consistent across all points of the shape.

Shape, size, orientation, and angle measures are all preserved under translation — only position changes, which means the translated shape is congruent to the original, an important geometric concept.

Understanding translation as adding constants to coordinates gives students an algebraic framework for all rigid transformations (reflections, rotations) studied in 6th–8th grade geometry.