Question

What are the polar coordinates of a point with $(-3,3)$ rectangle coordinates?

• A. $(3,{135}^{\circ })$
• B. $(-3,{135}^{\circ })$
• C. $(3\sqrt{2},{45}^{\circ })$
• D. $(3\sqrt{2},{135}^{\circ })$
• E. $(-3\sqrt{2},{45}^{\circ })$

Answer 1

The correct option is D $(3\sqrt{2},{135}^{\circ })$

Given the points $(-3,3)$

rectangular coordinates to polar coordinates,

$(x,y)⟶(r,\theta )r=\sqrt{x^2+x^2}=\sqrt{9+9}=3\sqrt{2}\tan \theta =\frac{y}{x}⟹\tan \theta =\frac{3}{-3}⟹\theta ={\tan }^{-1}(-1)=\frac{3\pi }{4}or\frac{7\pi }{4}$

As (-3,3) lies in I Quadrant, $\theta =3\frac{\pi }{4}(r,\theta )⟹(3\sqrt{2,},\frac{3\pi }{4})or,(3\sqrt{2},135°)$