An equilateral triangle has each side equal to

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

a

. If the coordinates of its vertices are

(x_1, y_1)

(x_2, y_2)

and

(x_3, y_3)

then the square of the determinant

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

equals (1)

3a^4

(2)

\frac{3a^4}{2}

(3)

\frac{3}{4}a^4

(4)

\frac{3}{8}a^4