Area of triangle using coordinates for JEE

Formula

\(\Delta=\dfrac12\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|\)

Variables: Vertices are \((x_1,y_1),(x_2,y_2),(x_3,y_3)\).

Collinearity, centroid, triangle geometry, locus.