Question

The polar co-ordinates of the points whose cartesian co-ordinates are as $(-2,-2)$, are

• A. $(2\sqrt{2},\frac{\pi }{4})$
• B. $(2\sqrt{2},\frac{5\pi }{4})$
• C. $(4,\frac{\pi }{4})$
• D. $(4,\frac{-3\pi }{4})$

Answer 1

Answer: (B)

$(2\sqrt{2},\frac{5\pi }{4})$

Cartesian coordinate is $(-2,-2)$
$r=\sqrt{x^2+y^2}$
$\Rightarrow r=2\sqrt{2}$
Also, $\tan \theta =\frac{y}{x}$
$\Rightarrow \tan \theta =1$
$\Rightarrow \theta =\frac{\pi }{4}$
Since, the point $(-2,-2)$ lies in third quadrant.
So, $\theta =\pi +\frac{\pi }{4}$
$\Rightarrow \theta =\frac{5\pi }{4}$
Hence, the polar form of $(-2,-2)$ is $(2\sqrt{2},\frac{5\pi }{4}).$