Add the same vector to every point: (x,y) → (x+a, y+b).
Key formulas
Rigid motion
Lengths and angles stay the same. Only position changes.
Example
Vector (3,−2) sends (1,4) to (4,2) and (0,0) to (3,−2).
Inverse
The inverse translation is (−a,−b). Doing both returns every point home.
Worked example
Worked example
Problem. Translate the point (5, −1) by vector (−2, 7).
Solution. (5, −1) + (−2, 7) = (3, 6).
Shape test
Translate all vertices; the image is congruent.
Review quiz
What vector maps (3,3) to (0,8)?
Practice questions
- Translate (5,−1) by (−2,7).
- What vector maps (3,3) to (0,8)?
Study notes
Is translation a matrix?
In pure 2D Cartesian form, addition is enough; matrices need homogeneous coordinates.