What is the Number Plane?
Have you ever used a map with a grid to find a location? Coordinate geometry works in a very similar way , it gives every single point in space a unique address using two numbers.
Number Plane: A flat surface (a grid) where every point can be described using two number lines , one horizontal and one vertical. It is also sometimes called the Cartesian plane or coordinate plane, named after the French mathematician René Descartes who invented this system in the 17th century , a great example of how one idea changed mathematics forever.
The number plane is built from two special number lines called axes (the singular is axis):
- The x-axis is the horizontal line (runs left–right)
- The y-axis is the vertical line (runs up–down)
These two axes cross each other at a very important point:
Origin: The point where the x-axis and y-axis meet. It is labelled O and has the coordinates (0, 0).
Think of the number plane like the streets of a city built on a perfect grid. The x-axis is like the main street running east–west, and the y-axis is the main street running north–south. The origin is the town centre where both main streets cross. Every address in the city is found by saying how far along and how far up you go from the centre.
Coordinates , The Address of a Point
Every point on the number plane has a unique address written as a pair of numbers.
Coordinates: A pair of numbers written as that describes the exact position of a point on the number plane. The first number is the x-coordinate (horizontal position) and the second is the y-coordinate (vertical position).
Coordinates are always written as an ordered pair in brackets with a comma between them:
The order matters , swapping the two numbers will take you to a completely different point!
How to read coordinates:
- The x-coordinate tells you how far to move left or right from the origin along the x-axis
- The y-coordinate tells you how far to move up or down from the origin along the y-axis
A helpful memory trick: "Along the corridor, then up (or down) the stairs." Always read the x-coordinate first (walk along the corridor), then read the y-coordinate (climb the stairs). You go across before you go up!
Reading coordinates
For the point A(3, 5):
- Step 1: Start at the origin O(0, 0)
- Step 2: Move 3 units to the right along the x-axis (x = 3)
- Step 3: Move 5 units upward from there (y = 5)
- Step 4: Mark and label the point A
For the point B(0, 4):
- Step 1: Start at the origin
- Step 2: Move 0 units along the x-axis (stay on the y-axis!)
- Step 3: Move 4 units upward
- B lies on the y-axis
For the point D(3, 0):
- Step 1: Start at the origin
- Step 2: Move 3 units to the right
- Step 3: Move 0 units up (stay on the x-axis!)
- D lies on the x-axis
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