Question

Which of the following is the formula for finding the area of a triangle with the vertices (x1,y1), (x2,y2), (x3,y3).

(a) Δ=\(\begin{Vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{Vmatrix}\)

(b) Δ=\(\frac{1}{2}\begin{Vmatrix}x_1&y_1&1\\x_2&y_2&0\\x_3&y_3&1\end{Vmatrix}\)

(c) Δ=\(\frac{1}{2}\begin{Vmatrix}x_1&y_1&1\\x_2&1&1\\x_3&y_3&1\end{Vmatrix}\)

(d) Δ=\(\frac{1}{2}\begin{Vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{Vmatrix}\)

The question was asked in class test.

Question is from Area of a Triangle in section Determinants of Mathematics – Class 12

Answer 1

The correct choice is (d) Δ=\(\frac{1}{2}\begin{Vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{Vmatrix}\)

Easy explanation: The area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) is given by

Δ=\(\frac{1}{2}\begin{Vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{Vmatrix}\).