Determine two pairs of polar coordinates for the point with 0° ≤ θ

Question

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°.
-$( 4 , - 4 )$
A) $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 45 ^ { \circ } \right)$
B) $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 225 ^ { \circ } \right)$
C) $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 135 ^ { \circ } \right)$
D) $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 315 ^ { \circ } \right)$

Quizplus · Accepted Answer

The point (4, -4) in Cartesian coordinates corresponds to a polar coordinate with a radius of $4\sqrt{2}$ and an angle of 315° (since it is in the fourth quadrant). The equivalent polar coordinate with a negative radius is $-4\sqrt{2}$ at 135°.

Determine Two Pairs of Polar Coordinates for the Point with 0°