Coordinates
3.1 Coordinates – Cheat Sheet
1. Cartesian Coordinates Basics
- Written as (x, y)
- x = horizontal distance from origin (left/right)
- y = vertical distance from origin (up/down)
- Origin: (0, 0)
- First value = move along x-axis
- Second value = move along y-axis
2. The Four Quadrants
| Quadrant | x-value | y-value | Example Point |
|---|---|---|---|
| I | + | + | (3, 5) |
| II | − | + | (−4, 2) |
| III | − | − | (−2, −6) |
| IV | + | − | (5, −3) |
3. Plotting Points
- Start at origin (0, 0).
- Move along x-axis first (positive → right, negative → left).
- Move along y-axis next (positive → up, negative → down).
Example: (−3, 4) → Move 3 left, 4 up.
4. Reading Coordinates from a Graph
- Identify x-value from horizontal axis.
- Identify y-value from vertical axis.
- Write as ordered pair (x, y).
5. Midpoint Formula
For points (x₁, y₁) and (x₂, y₂):
Midpoint = ( (x₁ + x₂) / 2 , (y₁ + y₂) / 2 )
Example: (2, 5) and (6, 9) → Midpoint = ( (2 + 6)/2 , (5 + 9)/2 ) = (4, 7)
6. Examples Table for Quick Reference
| Task | Example | Answer |
|---|---|---|
| Plot point | (4, −2) | 4 right, 2 down |
| Quadrant | (−5, −1) | Quadrant III |
| Midpoint of (2, 3) & (8, 5) | ((2+8)/2 , (3+5)/2) | (5, 4) |