Orientation Math Example 1

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

Example 1

easy
A triangle has vertices listed counterclockwise as A, B, C. After a reflection, the vertices appear clockwise. Has the orientation changed?

Solution

  1. 1
    Step 1: Orientation refers to whether vertices go clockwise or counterclockwise.
  2. 2
    Step 2: Original: A→B→C counterclockwise (positive orientation).
  3. 3
    Step 3: After reflection: A→B→C clockwise (negative orientation).
  4. 4
    Step 4: Yes, the orientation has reversed.

Answer

Yes, the orientation changed from counterclockwise to clockwise.
Reflections always reverse orientation. Rotations and translations preserve orientation. A figure has positive orientation if its vertices are listed counterclockwise, and negative if clockwise.

About Orientation

Orientation is the directional sense of a geometric figure — whether its vertices are ordered clockwise or counterclockwise. It describes how a shape is 'facing' in space, and is preserved by rotations and translations but reversed by reflections.

Learn more about Orientation →

More Orientation Examples

Example 2 medium

Vertices of triangle ABC are at [formula], [formula], [formula]. Using the signed area formula, dete

Example 3 easy

Does a 90° rotation change the orientation of a figure?

Example 4 hard

A left-handed glove is reflected in a mirror. Can the reflected image be rotated in 3D to match the

← All Orientation Examples Orientation Concept