APFIVE Identifying Quadrants From Polar Coordinates
The table provides the polar coordinates $$(r, \theta)$$ for four points.
| Point | A | B | C | D |
|---|---|---|---|---|
| $$r$$ | 2 | 2 | -2 | -2 |
| $$\theta$$ | $$-\tfrac{\pi}{4}$$ | $$-\tfrac{3\pi}{4}$$ | $$\tfrac{5\pi}{4}$$ | $$\tfrac{7\pi}{4}$$ |
Which point lies in Quadrant II of the $$xy$$-plane?
A
D, because from the positive x-axis, $$\frac{7\pi}{4}$$ counterclockwise from the origin is in Quadrant IV, and the negative radius indicates the opposite direction of the angle from the origin.
B
A, because from the positive y-axis, $$\frac{\pi}{4}$$ counterclockwise is in Quadrant II, and the radius is positive.
C
C, because from the positive x-axis, $$\frac{5\pi}{4}$$ counterclockwise is in Quadrant III, and the negative radius indicates a reflection over the x-axis.
D
B, because from the positive x-axis, $$\frac{3\pi}{4}$$ clockwise is in Quadrant II, and the radius is positive.
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