Rotation Math Example 3

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

Example 3

easy
What is the image of point (0,5)(0, 5) after a 180°180° rotation about the origin?

Solution

  1. 1
    Step 1: A 180° rotation maps (x,y)→(−x,−y)(x, y) \to (-x, -y).
  2. 2
    Step 2: (0,5)→(0,−5)(0, 5) \to (0, -5).

Answer

(0,−5)(0, -5)
A 180° rotation moves every point to the opposite side of the origin, the same distance away. For a point on the y-axis like (0,5)(0, 5), it maps to (0,−5)(0, -5) — directly opposite on the y-axis. This is equivalent to negating both coordinates.

About Rotation

A rigid transformation that turns every point of a figure by a fixed angle around a fixed center of rotation.

Learn more about Rotation →

More Rotation Examples

Example 1 easy

Rotate the point [formula] by [formula] counterclockwise about the origin. Where does A end up?

Example 2 medium

Rotate the point [formula] by [formula] counterclockwise about the origin. Give exact coordinates.

Example 4 hard

Triangle with vertices [formula], [formula], [formula] is rotated [formula] CCW about the point [for

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