Mathematics · essential
Area of triangle from coordinates for JEE
Area of triangles using determinants
Formula
\[\text{Area}=\frac{1}{2}\left|\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}\right|=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\]
Variables: \((x_1,y_1),(x_2,y_2),(x_3,y_3)\): vertices of triangle.
Conditions: Points lie in a plane.
Coordinate geometry and determinant-based area questions.