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

Question

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 5,5 )$
A) $\left( 5 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 315 ^ { \circ } \right)$

B) $\left( 5 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 45 ^ { \circ } \right)$

C) $\left( 5 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 135 ^ { \circ } \right)$

D) $\left( 5 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 225 ^ { \circ } \right)$

Quizplus · Accepted Answer

The point (5,5) in Cartesian coordinates is located in the first quadrant, where both x and y are positive and equal. This means the angle from the positive x-axis is 45 degrees. The polar coordinate radius can be found using the Pythagorean theorem, $r = \sqrt{x^2 + y^2} = \sqrt{5^2 + 5^2} = 5\sqrt{2}$. The first pair is $(5\sqrt{2}, 45^\circ)$. For the second pair, adding 180 degrees to the angle gives a direction pointing in the opposite direction with the same radius, but since polar coordinates can have negative radius values, the equivalent point is $(-5\sqrt{2}, 225^\circ)$.

Determine Two Pairs of Polar Coordinates for the Point With 0