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# Which point is located in Quadrant III ? \begin{aligned} & \circ\left(-\frac{1}{2}, \frac{1}{4}\right) \\ & \circ\left(\frac{1}{2},-\frac{1}{4}\right) \\ & \circ\left(-\frac{1}{2},-\frac{1}{4}\right) \end{aligned} I don't know.
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Answer

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Step 1:
I'll solve this step by step using the quadrant rules and LaTeX formatting.

Step 2:
: Recall the quadrant rules

- Quadrant I: (+x, +y) - Quadrant II: (-x, +y) - Quadrant III: (-x, -y) - Quadrant IV: (+x, -y)

Step 3:
: Analyze the first point \left(-\frac{1}{2}, \frac{1}{4}\right)

- x-coordinate is negative: $$-\frac{1}{2}
- y-coordinate is positive: \frac{1}{4} - This point is in Quadrant II

Step 4:
: Analyze the second point \left(\frac{1}{2},-\frac{1}{4}\right)

- x-coordinate is positive: $$\frac{1}{2}
- y-coordinate is negative: -\frac{1}{4} - This point is in Quadrant IV

Step 5:
: Analyze the third point \left(-\frac{1}{2},-\frac{1}{4}\right)

- x-coordinate is negative: $$-\frac{1}{2}
- y-coordinate is negative: -\frac{1}{4} - This point is in Quadrant III

Final Answer

The point \left(-\frac{1}{2},-\frac{1}{4}\right) is located in Quadrant III.