Coordinate (Copy)

Cartesian Coordinates Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Using and Interpreting Cartesian Coordinates in Two Dimensions

1. What Are Cartesian Coordinates?

• A coordinate system using two perpendicular number lines:
  • x-axis (horizontal)
  • y-axis (vertical)
• A point is written as an ordered pair:
  (x, y)
  → x = horizontal position (left/right)
  → y = vertical position (up/down)

2. The Four Quadrants

• The point (0, 0) is called the origin

3. Plotting Points

• Start from the origin (0, 0)
• Move:
  • Right if x is positive, left if x is negative
  • Up if y is positive, down if y is negative

Example: Plot (–2, 3)
→ Move 2 units left, then 3 units up

4. Reading Coordinates from a Graph

• Locate the point on the grid
• Read the x-value from the horizontal axis
• Read the y-value from the vertical axis
• Write as (x, y)

5. Midpoint Formula (Optional but Useful)

• Midpoint between A(x₁, y₁) and B(x₂, y₂):

  (x1+x22,y1+y22)left( frac{x₁ + x₂}{2}, frac{y₁ + y₂}{2} right)

6. Exam Tasks You Might See

• Plotting points on a grid
• Identifying coordinates of a point
• Naming the quadrant of a point
• Finding distance between points (counting squares)
• Describing movements (e.g., translation: right 3, up 2)

7. Common Mistakes to Avoid

• Reversing x and y (always write x first!)
• Getting quadrant signs wrong
• Miscounting squares on grid axes

Key Tip:

Remember:
“x is left-right, y is up-down”
Always label axes when plotting.