Ever wondered how a map app knows exactly where you are?

When Ngozi shares her location, her phone sends two numbers, not a long description. Two numbers are enough to pin down any spot — and the Cartesian plane shows you how.

📒 The Cartesian Plane: lesson notes

Meet the x-axis, the y-axis, the origin and the four quadrants, and read the coordinates of any point.

When Ngozi shares her location, her phone sends two numbers, not a long description. Two numbers are enough to pin down any spot — and the Cartesian plane shows you how.

Two number lines

The Cartesian plane is made from two number lines that cross at right angles.

The horizontal line is the x-axis; the vertical line is the y-axis. They cross at the origin, the point (0, 0).

On the x-axis, right is positive and left is negative. On the y-axis, up is positive and down is negative.

🔑 Key idea: x-axis across, y-axis up and down, meeting at the origin (0, 0).

Coordinates: (x, y)

Every point has an address called its coordinates, written (x, y). The first number, x, tells you how far to go across; the second number, y, tells you how far to go up or down.

The point (4, −3) is 4 units right and 3 units down from the origin.

Order matters: (2, 5) and (5, 2) are different points. Remember: x comes before y, just as in the alphabet.

A point with a 0 sits on an axis: (6, 0) is on the x-axis and (0, −2) is on the y-axis.

🔑 Key idea: (x, y): across first, then up or down.

The four quadrants

The axes cut the plane into four quadrants, numbered anticlockwise from the top right.

First (+, +) top right; second (−, +) top left; third (−, −) bottom left; fourth (+, −) bottom right.

So (−3, 5) is in the second quadrant because x is negative and y is positive.

🔑 Key idea: Use the signs of x and y to find the quadrant.

Worked example

In which quadrant is the point (−2, 3)?

Step 1: Read the signs
x = −2 is negative, so go left.
y = 3 is positive, so go up.
Step 2: Name the quadrant
top left → second quadrant, signs (−, +)
Why? The quadrants are numbered anticlockwise, starting from the top right.

Answer: Second quadrant

Summary

The x-axis is horizontal, the y-axis is vertical, and they meet at the origin (0, 0).
Coordinates are written (x, y): across first, then up or down.
Right and up are positive; left and down are negative.
Quadrants: first (+, +), second (−, +), third (−, −), fourth (+, −).
A point with a 0 coordinate lies on an axis.

Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.