The rectangular coordinates of a point are given. Find polar coordinates for the point.
-(-3, 3)
A) $\left( 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
B) $\left( - 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
C) $\left( - 3 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
D) $\left( 3 \sqrt { 2 } , \frac { 3 \pi } { 4 } \right)$

Question

The rectangular coordinates of a point are given. Find polar coordinates for the point.
-(-3, 3) 
A) $\left( 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
B) $\left( - 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
C) $\left( - 3 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
D) $\left( 3 \sqrt { 2 } , \frac { 3 \pi } { 4 } \right)$

Quizplus · Accepted Answer

The polar coordinates $(r, \theta)$ of a point with rectangular coordinates $(x, y)$ are given by $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the point $(-3, 3)$, $r = \sqrt{(-3)^2 + 3^2} = 3\sqrt{2}$, and $\theta = \tan^{-1}\left(\frac{3}{-3}\right) = \tan^{-1}(-1)$, which is $\frac{3\pi}{4}$ in the second quadrant.

The Rectangular Coordinates of a Point Are Given (32,−3π4)\left( 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)(32​,−43π​)

The Rectangular Coordinates of a Point Are Given $\left( 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$