Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$
- $( 0 , - \sqrt { 5 } )$

Question

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 0 , - \sqrt { 5 } )$
A) $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 0 ^ { \circ } \right)$
B) $\left( \sqrt { 5 } , 270 ^ { \circ } \right) , \left( - \sqrt { 5 } , 90 ^ { \circ } \right)$
C) $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 270 ^ { \circ } \right)$
D) $\left( \sqrt { 5 } , 0 ^ { \circ } \right) , \left( - \sqrt { 5 } , 180 ^ { \circ } \right)$

Quizplus · Accepted Answer

The point $(0, -\sqrt{5})$ is located on the negative y-axis. The correct polar coordinates are $\left(\sqrt{5}, 270^\circ\right)$ because the radius is the distance from the origin, which is $\sqrt{5}$, and the angle $270^\circ$ points directly downward. The second pair, $\left(-\sqrt{5}, 90^\circ\right)$, represents the same point because a negative radius $-\sqrt{5}$ with an angle of $90^\circ$ effectively points in the opposite direction (downwards), which also locates the point at $(0, -\sqrt{5})$.

Determine Two Pairs of Polar Coordinates for the Point With 0