Translation just slides a shape — every point moves the same distance in the same direction. No turning, no flipping, no resizing. The before and after are identical, only relocated.
Slide the shape
Slide: (3, 1)
original image
Translation by a vector
The vector (a, b) — 'a right, b up' — is added to every point of the shape.
Facts about sliding
- Everything is preserved: lengths, angles, area, *and* orientation. The image is congruent and not mirrored — the strongest kind of 'same'.
- There are no fixed points (unless the vector is zero) — the whole plane shifts.
- Two translations done in a row make another translation — just add the vectors.
- A translation is what you get from two reflections in parallel mirror lines.
Your turn
Translate the triangle with vertices (1, 1), (3, 1), (2, 4) by the vector (−2, 3). Where do the vertices go?