Question

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

A) (4√2, 45°), (-4√2, 225°)

B) (4√2, 135°), (-4√2, 315°)

C) (4√2, 225°), (-4√2, 45°)

D) (4√2, 315°), (-4√2, 135°)

Answer 1

The point (4, -4) lies in Quadrant IV. Since we are interested only in positive angles, we choose 315 degrees with a radius (magnitude) of 4√2. That automatically eliminates Answer Choices A, B and C, so all we have to do now is to verify that (-4√2, 135 degrees) also represents (4, -4). It does: Going to Quadrant II with angle 135 degrees, and then using -4√2 as the magnitude, takes us to Quadrant IV.

Thus, D is the correct answer.