Translation Math Example 5

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

Example 5

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

Solution

  1. 1
    Step 1: The bottom-left corner (1,1)(1,1) must go to (0,0)(0,0). Translation vector =(0−1, 0−1)=(−1,−1)= (0-1,\ 0-1) = (-1,-1).
  2. 2
    Step 2: Apply (−1,−1)(-1,-1) to all vertices: (1,1)→(0,0)(1,1)\to(0,0); (3,1)→(2,0)(3,1)\to(2,0); (3,3)→(2,2)(3,3)\to(2,2); (1,3)→(0,2)(1,3)\to(0,2).
  3. 3
    Step 3: New square: (0,0),(2,0),(2,2),(0,2)(0,0), (2,0), (2,2), (0,2).

Answer

Translation vector (−1,−1)(-1,-1); new vertices: (0,0),(2,0),(2,2),(0,2)(0,0), (2,0), (2,2), (0,2).
When repositioning a figure so one specific point lands on a target, compute the translation vector from that point to the target, then apply it uniformly to all vertices. The shape, size, and orientation of the square are all unchanged.

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 1 easy

Translate the point [formula] by the vector [formula]. Where does A end up?

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?

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