An equilateral triangle has each side equal to \( a \). If the co-o...

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An equilateral triangle has each side equal to \( a \). If the co-ordinates of its vertices are \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and
W \( \left(x_{3}, y_{3}\right) \), show that :
\[
\left|\begin{array}{lll}
x_{1} & y_{1} & 1 \\
x_{2} & y_{2} & 1 \\
x_{3} & y_{3} & 1
\end{array}\right|^{2}=\frac{3 a^{4}}{4} .
\]
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