X Tables
geometry

Coordinates in four quadrants

Extend coordinate grids to negative numbers.

Quick answer

Coordinates in four quadrants are a way to describe where points are on a grid using numbers, including negative numbers. You write them as (x, y) where x is the horizontal position and y is the vertical position. The grid is split into four sections called quadrants, and negative numbers help us describe positions in all directions.

Learning outcome

By the end of this page, you will be able to plot and read coordinates in all four quadrants of a grid, including negative numbers. Success signs:
  • You can read coordinates like (-3, 4) and (-5, -2)
  • You can plot points in any quadrant
  • You understand that negative numbers go left and down
  • You can use coordinates to describe positions in real life

Why this matters

Coordinates help us find exact places on a map, plan where to build in games, and understand how things move in space. When you play games like Monopoly, Chess, or even Connect Four, you're using a kind of coordinate system. In real life, you might use coordinates to find your way around a big shopping mall, or to describe where your pet dog is hiding in the garden.

How it works

Let’s start with a normal grid, like the one you might use in class. This grid has two lines that cross each other – one horizontal (called the x-axis) and one vertical (called the y-axis). Usually, we only look at positive numbers, but now we’ll include negative numbers too. The grid is divided into four parts called quadrants:
  1. Quadrant 1: Top right (both x and y are positive)
  2. Quadrant 2: Top left (x is negative, y is positive)
  3. Quadrant 3: Bottom left (both x and y are negative)
  4. Quadrant 4: Bottom right (x is positive, y is negative)
To find a point like (-3, 4):
  1. Start at the middle (0, 0)
  2. Move 3 spaces to the left (because x is -3)
  3. Move 4 spaces up (because y is 4)

Examples you can see

Let’s look at a few points to help you understand how this works.
Point Quadrant How to get there
(2, 3) Quadrant 1 Move 2 right, 3 up
(-2, 3) Quadrant 2 Move 2 left, 3 up
(-2, -3) Quadrant 3 Move 2 left, 3 down
(2, -3) Quadrant 4 Move 2 right, 3 down
Let’s imagine a treasure hunt in your garden. The treasure is hidden at (-4, 5). That means:
  • Start at the middle of your garden
  • Walk 4 steps to the left
  • Then walk 5 steps forward (up)

Try it as a mini adventure

Adventure: The Lost Treasure Hunt You are a treasure hunter in a magical garden. Your map shows the treasure is hidden at coordinates (-3, -5). Here’s your quest:
  1. Start at the middle of the garden (0, 0)
  2. Walk 3 steps to the left
  3. Then walk 5 steps down
  4. Look for the treasure!
Draw your garden grid and mark where the treasure is. Try plotting a few more points:
  • Point A: (1, 2)
  • Point B: (-1, -2)
  • Point C: (4, -1)

Common mistakes

  • Mistake: Thinking x comes first, then y, but mixing them up.
    Why it happens: It’s easy to get confused when you first learn this.
    Fix: Remember: "x is the horizontal, y is the vertical" or "x comes first, like in the alphabet".
  • Mistake: Confusing which direction negative numbers go.
    Why it happens: You might think negative numbers go up or right.
    Fix: Negative x goes left, negative y goes down.
  • Mistake: Forgetting that coordinates are written as (x, y).
    Why it happens: It’s a new way of thinking.
    Fix: Practice writing and reading (x, y) pairs with your parent or teacher.

Parent and carer guide

You can help your child by:
  • Using a simple grid to draw and plot points together
  • Playing games that use coordinates, like Battleship
  • Looking for coordinates in everyday life: like on maps, or in video games
  • Practicing with a number line to understand negative numbers
  • Encouraging your child to draw their own grid and label the quadrants
If your child gets confused, take a deep breath and go back to the basics:
  • Start with (0, 0) in the middle
  • Count steps carefully
  • Use a pencil to mark the points
Don’t worry if it takes time to get used to negative numbers – that’s normal!

Practice questions

  1. Which quadrant is the point (4, -2) in?
  2. Plot the point (-1, 3)
  3. What are the coordinates of a point that is 5 steps to the left and 3 steps up?
  4. Which quadrant is (-5, -4) in?
  5. Plot the point (0, -3)
Answers:
  1. Quadrant 4
  2. Plot 1 step left, 3 steps up
  3. (-5, 3)
  4. Quadrant 3
  5. Plot 3 steps down from the middle

FAQ

What are coordinates?

Coordinates are a pair of numbers (x, y) that tell us exactly where a point is on a grid.

Why do we need negative numbers in coordinates?

Negative numbers help us describe positions in all directions – left, right, up, and down – not just one way.

How do I remember which quadrant is which?

You can think of the quadrants like a clock: Quadrant 1 is top right, then go clockwise to Quadrant 2, 3, and 4.

Can I use coordinates in real life?

Yes! You can use coordinates to find your way around a map, or to play games like Connect Four or Battleship.

What if I get confused with x and y?

Try saying "x is horizontal, y is vertical" or use a memory trick like "x comes first like in the alphabet".