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°.
-$( 0 , \sqrt { 7 } )$
A) $\left( 7,90 ^ { \circ } \right) , \left( - 7,270 ^ { \circ } \right)$
B) $\left( \sqrt { 7 } , 270 ^ { \circ } \right) , \left( - \sqrt { 7 } , 90 ^ { \circ } \right)$
C) $\left( 7,0 ^ { \circ } \right) , \left( - 7,180 ^ { \circ } \right)$
D) $\left( \sqrt { 7 } , 90 ^ { \circ } \right) , \left( - \sqrt { 7 } , 270 ^ { \circ } \right)$

Quizplus · Accepted Answer

The point $(0, \sqrt{7})$ in Cartesian coordinates corresponds to a point directly above the origin on the y-axis at a distance of $\sqrt{7}$. In polar coordinates, this translates to a radius of $\sqrt{7}$ and an angle of $90^\circ$ for the positive radius. For the negative radius, the point can be represented as having a radius of $-\sqrt{7}$ but now pointing downwards, which corresponds to an angle of $270^\circ$.

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