Translation Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

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

Solution

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

Answer

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

About Translation

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

Learn more about Translation →

More Translation Examples

Example 2 medium

Triangle with vertices [formula], [formula], [formula] is translated by [formula]. Find the new vert

Example 3 medium

Triangle with vertices [formula], [formula], [formula] is translated by [formula]. Find the new vert

Example 4 easy

Point [formula] is translated to [formula]. What is the translation vector?

Example 5 hard

A square with vertices [formula], [formula], [formula], [formula] is translated so that the bottom-l

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