Mathematics · JEE | DETERMINANTS

What is the area of a triangle with vertices \( (x_1, y_1), (x_2, y_2), \) and \( (x_3, y_3) \)?

1. A
   \( \Delta = 2 \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix} \)
2. B
   \( \Delta = \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix} \)
3. C
   \( \Delta = \frac{1}{3} \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix} \)
4. D
   \( \Delta = \frac{1}{2} \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix} \)