State the sign (positive or negative) of the determinant when the vertices

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

State the sign (positive or negative) of the determinant

\det\begin{pmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{pmatrix}

when the vertices

(x_1,y_1)

(x_2,y_2)

and

(x_3,y_3)

of a triangle are taken in counter-clockwise order.