Answer
C
Work Step by Step
Consider the given polar coordinate $\left( -3,\frac{\pi }{4} \right)$ as $\left( r,\theta \right)$.
Here,
$\begin{align}
& \theta =\frac{\pi }{4} \\
& r<0 \\
\end{align}$
From above, it is clear that $\theta $ has been taken in the counter clockwise direction and
$r<0$, so $r$ lies opposite to the terminal side.
Hence, $\left( -3,\frac{\pi }{4} \right)$ coordinate lies in the third quadrant.
