Area of Triangle

The determinant also gives a compact formula for the area of a triangle whose vertices are known coordinates. For a triangle with vertices $A(x_1, y_1)$, $B(x_2, y_2)$ and $C(x_3, y_3)$,

Since an area can never be negative, always take the absolute value of this determinant; if the area is given and you're solving for an unknown coordinate instead, both the positive and negative values of the determinant should be considered as valid algebraic cases. A special consequence follows immediately: if this determinant evaluates to exactly zero, the triangle then has no are …