Definition:Sign of Area of Triangle/Definition 2
Jump to navigation
Jump to search
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 $P$.
- Triangle $\triangle ABC$ with Positive Area
- Triangle $\triangle ABC$ with Negative Area
Also see
Sources
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $7$. Sign of an area