Quickly recall the sign conventions for the four quadrants. A simple mnemonic is to think about moving right/left (for x) and up/down (for y) from the origin. For Quadrant IV, you move right (positive x) and down (negative y).
The relationship cannot be determined from the information given
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The Correct Option isA
Solution and Explanation
Step 1: Understanding the Concept:
This question tests knowledge of the Cartesian coordinate system, specifically the signs of coordinates in each quadrant. Step 2: Detailed Explanation:
The point P(a,b) is located in the fourth quadrant. The quadrants are numbered counter-clockwise starting from the top right.
- Quadrant I: x is positive, y is positive (+,+).
- Quadrant II: x is negative, y is positive (-,+).
- Quadrant III: x is negative, y is negative (-,-).
- Quadrant IV: x is positive, y is negative (+,-).
Since P(a,b) is in the fourth quadrant, its x-coordinate, \(a\), must be positive, and its y-coordinate, \(b\), must be negative.
\[ a \textgreater 0 \quad \text{and} \quad b \textless 0 \]
Step 3: Comparing the Quantities:
We are comparing Column A (\(a\), a positive number) with Column B (\(b\), a negative number).
Any positive number is always greater than any negative number.
Therefore, \(a \textgreater b\), and the quantity in Column A is greater.
