Definition
Translation
A translation slides every point the same distance in the same direction.
What it means
A translation is a slide with no turn, flip, or resize. Pick any point on the shape: its matching point moves by the same arrow as every other point. On a grid, “4 right and 2 up” must be done to every vertex.
Remember it
Same arrow for every point.
Example
Triangle A(1, 1), B(3, 1), C(2, 3) is translated by ⟨4, 2⟩. Add 4 to every x-coordinate and 2 to every y-coordinate. The image is A′(5, 3), B′(7, 3), C′(6, 5), with the same side lengths and the same orientation.
Watch for
A move that turns, flips, or changes the size is not a translation, even if the figure also changes position.
Common mix-up
In ordinary English, translation can mean changing words from one language to another. Here it means the geometry slide.
Exact meaning
A translation is a rigid transformation that adds one fixed displacement vector to every point. Every point moves the same distance in the same direction, so lengths, angles, parallelism, size, and orientation are preserved.