What are the Four Quadrants? The two perpendicular axes divide the plane into four quadrants, numbered counterclockwise starting from the top-right.
| Quadrant | x-sign | y-sign | Example point |
|---|---|---|---|
| Quadrant I (Q1) | + | + | (3, 4) |
| Quadrant II (Q2) | - | + | (-3, 4) |
| Quadrant III (Q3) | - | - | (-3, -4) |
| Quadrant IV (Q4) | + | - | (3, -4) |
Points on Axes:
- On X-axis: \(y = 0\), e.g., \((5, 0)\), \((-2, 0)\)
- On Y-axis: \(x = 0\), e.g., \((0, 3)\), \((0, -4)\)
- Origin: \((0, 0)\) (on both axes)
Distance Interpretation:
- The x-coordinate tells how far a point is from the Y-axis
- The y-coordinate tells how far a point is from the X-axis
- The distance from the origin = \(\sqrt{x^2 + y^2}\) (Pythagorean theorem)
Distance between two points:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Horizontal and Vertical Distances:
- Same y-coordinate → horizontal distance = \(|x_2 - x_1|\)
- Same x-coordinate → vertical distance = \(|y_2 - y_1|\)