What Is a Translation?

What stays the same

Because every point travels the same distance in the same direction, the original figure and its image remain congruent. Corresponding segments such as AA' and BB' are parallel and equal in length, which is one of the fastest ways to verify a translation on a graph.

This page keeps the preimage and image visible together so translation can be read as a uniform slide on the plane rather than as a coordinate rule learned in isolation.

For a translation by (3, -2), every point moves three units right and two units down. The shape does not need a special starting location; the same vector works at every vertex. Checking two or three corresponding arrows is a quick way to catch a point that was moved by a different amount.

• A translation slides a figure without turning or resizing it.
• A nonzero translation preserves lengths, angle measures, and orientation, so it is a rigid motion.
• Every point in the figure moves by the same horizontal and vertical change.
• Translation can be described by a vector or by coordinate changes such as adding the same pair to every vertex.

Where translations help

• Use translation when plotting image points from a given vector or ordered-pair shift.
• Use it in symmetry and tessellation work where a shape repeats by sliding across the plane.
• Use it when reading coordinate rules such as left-right and up-down movements without any change in size.

Translation checks to make

• Do not call a motion a translation if the figure has turned or flipped at the same time.
• Do not move only one vertex by the stated amount; every point must follow the same displacement.
• Do not mix the horizontal change with the vertical change when writing the coordinate rule.