Translation Math Example 2

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

Example 2

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

Solution

  1. 1
    Step 1: Translate each vertex by (−2,3)(-2, 3): A′=(−2,3)A'=(-2,3); B′=(1,3)B'=(1,3); C′=(−2,7)C'=(-2,7).
  2. 2
    Step 2: Verify AB=A′B′AB = A'B': AB=3AB = 3, A′B′=∣1−(−2)∣=3A'B' = |1-(-2)| = 3. ✓
  3. 3
    Step 3: Verify AC=A′C′AC = A'C': AC=4AC = 4, A′C′=∣7−3∣=4A'C' = |7-3| = 4. ✓
  4. 4
    Step 4: Side lengths are preserved — translation is an isometry.

Answer

A′(−2,3)A'(-2,3), B′(1,3)B'(1,3), C′(−2,7)C'(-2,7). Shape unchanged.
Translation is an isometry: it preserves all distances and angles. The triangle slides to a new position without any rotation, reflection, or size change. Every point moves by exactly the same vector.

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 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

← All Translation Examples Translation Concept