Numeracy

Cartesian Coordinate Systems: Basics





1. What Are Cartesian Coordinates?

  • Used to locate points in 1D, 2D, and 3D spaces.
  • A point represents a unique position but has no size.
  • Points are described by coordinates relative to known reference axes.

Key Features:
- 2D Cartesian System: Described as (x, y).
- 3D Cartesian System: Described as (x, y, z).


2. Two-Dimensional Cartesian Coordinates

  • Defined by two perpendicular axes: x (horizontal) and y (vertical).
  • The point where x and y = 0 is called the origin (0,0).
  • Quadrants: The axes divide the plane into 4 quadrants (Q1 to Q4).

Key Tasks:
1. Determine Coordinates: For Point A (2,3), move 2 units along the x-axis and 3 units along the y-axis.
2. Locate a Point from Coordinates: For (?5.5,1.5), move left (x =5.5) and down (y =1.5).

Sequence Matters!
- Coordinates are always written as (x, y).
- Example: (2,3) (3,2).


3. Three-Dimensional Cartesian Coordinates

  • Adds a z-axis perpendicular to the x-y plane, representing height or depth.
  • Describes a point in space as (x, y, z).
  • Origin in 3D: (0,0,0).

Visualization Example:
- Holding a ball at shoulder height:
- Ground = x-y plane.
- Point where the ball bounces = (x, y).
- Height of the ball = z.


4. Applications of Cartesian Coordinates

a. Plotting Graphs

  • Used to represent algebraic equations visually.
  • Example: For (y = x^2 + 9x + 20), calculate y for each x and plot points (x, y).

b. Map Reading?

  • Grid References: Use eastings (x) and northings (y).
  • 4-Figure Grid: Locates a square (e.g., 1947).
  • 6-Figure Grid: Provides precise location (e.g., 203483).
  • How to Read: "Along the corridor (eastings), then up the stairs (northings)."

Example:
- Car park: 1947 (4-figure).
- Picnic site: 203483 (6-figure).


5. Key Takeaways

  • Cartesian coordinates are fundamental for graphing, spatial understanding, and navigation.
  • Order and accuracy in coordinates are critical to avoid confusion.
  • Understanding this system helps in real-life tasks like plotting data, navigation, and design.

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