Work out coordinate geometry area instantly with clear inputs, formula shown and shareable results.
The area of a triangle from coordinates is half the absolute value of the determinant x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂). The sign of that determinant reveals whether the vertices were listed clockwise or counter-clockwise.
Coordinate area
A = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
The three points lie on one straight line, so they enclose no area.
Not for the area, because of the absolute value, but it flips the sign of the determinant and hence the reported orientation.