Definition:Sign of Area of Triangle/Definition 2

Definition
Let $\triangle ABC$ be a triangle embedded in the plane.

Let the sides of $\triangle ABC$ be traversed in the order of its vertices, that is:
 * $AB \to BC \to CA$

If the area of $\triangle ABC$ is thus described in an anticlockwise direction, then $\triangle ABC$ is defined as having positive area.

If the area of $\triangle ABC$ is thus described in a clockwise direction, then $\triangle ABC$ is defined as having negative area.

Thus if a person $P$ were to walk around the boundary of $\triangle ABC$ in the direction $AB \to BC \to CA$ where $\triangle ABC$ has a positive area, the interior of $\triangle ABC$ would be on the left of $P$.


 * Positive-triangle.png


 * Triangle $\triangle ABC$ with Positive Area


 * Negative-triangle.png


 * Triangle $\triangle ABC$ with Negative Area

Also see

 * Equivalence of Definitions of Sign of Area of Triangle