A triangle has area 0 from its vertex coordinates. What does this indicate?

Given A$(x$₁, $y$₁), B$(x$₂, $y$₂), C$(x$₃, $y$₃), the area is:

**Area = $\frac{1}{2}|x$₁$(y$₂ − $y$₃) + $x$₂$(y$₃ − $y$₁) + $x$₃$(y$₁ − $y$₂)|**

The absolute value sign |·| ensures area is positive regardless of vertex order.

**Use case 1**: Compute area without drawing anything.
**Use case 2**: Test for COLLINEARITY — three points are collinear iff the (signed) area expression equals 0.

**Example**: A(1, 1), B(2, 3), C(4, 5).
Area = $\frac{1}{2}|1(3-5)+2(5-1)+4(1-3)|=\frac{1}{2}|-2+8-8|=\frac{1}{2}$·2 = 1.
Non-zero → not collinear.