Translation Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Translation.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A rigid transformation that slides every point of a figure the same distance in the same direction.

Sliding a chess piece straight across the board—every point moves the same amount, same direction.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Translation is a rigid motion that preserves size, shape, and orientation—only position changes.

Common stuck point: Every single point moves exactly the same distance in exactly the same direction—no rotation occurs.

Sense of Study hint: Pick any vertex and move it by the translation vector. Then move every other vertex by the exact same amount and direction.

Worked Examples

Example 1

easy
Translate the point A(2, -3) by the vector (5, 4). Where does A end up?

Solution

  1. 1
    Step 1: A translation by (a, b) maps (x, y) \to (x+a, y+b).
  2. 2
    Step 2: A(2, -3) translated by (5, 4): (2+5,\ -3+4) = (7, 1).
  3. 3
    Step 3: A' = (7, 1).

Answer

A' = (7, 1)
A translation slides every point by the same amount in the same direction. The translation vector (5, 4) means move 5 units right and 4 units up. Translations preserve distances, angles, and orientation — they are rigid motions.

Example 2

medium
Triangle with vertices A(0,0), B(3,0), C(0,4) is translated by (-2, 3). Find the new vertices and confirm the side lengths are unchanged.

Example 3

medium
Triangle with vertices A(1,2), B(4,2), C(3,5) is translated by \langle -3, 4 \rangle. Find the new vertices.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Point P(4, 7) is translated to P'(1, 3). What is the translation vector?

Example 2

hard
A square with vertices (1,1), (3,1), (3,3), (1,3) is translated so that the bottom-left corner moves to (0, 0). Find the new vertices and the translation vector.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

transformation geo