Describing positions in the four quadrants

Part of MathsCoordinatesYear 6Year 6

Grids with four quadrants

A grid can be divided into four sections called quadrants.

A grid with four quadrants can be used to display coordinates with positive and negative numbers.

A four quadrant grid. The both the x-axis and the y-axis stretch from -6 to 6.

Coordinates are always written like this (2, 3).

Coordinates contain two numbers. The first number shows the position on the x-axis and the second number shows the position on the y-axis.

This information can help you to find positions in all four quadrants on the grid.

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Activity: Describing positions in the four quadrants

Complete this interactive activity to understand how to describe positions in the four quadrants. Then put your knowledge to the test.

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Describing positions on a grid

A grid with four quadrants can have coordinates with positive and negative numbers.

The two axes on the grid meet at right angles at the point called the origin.

When reading coordinates, always read along the x-axis (the horizontal axis) first, then read up or down the y-axis (the vertical axis).

The origin, located at (0, 0), is where the x-axis and y-axis meet.

A four quadrant grid. The both the x-axis and the y-axis stretch from -6 to 6. The origin is highlighted as (0, 0)

The four quadrants are called the 'first quadrant', 'second quadrant', 'third quadrant' and 'fourth quadrant.

In the first quadrant, both coordinates are positive.

In the second and fourth quadrants, one number in the coordinate is negative.

In the third quadrant, both numbers are negative.

A four quadrant grid. The four quadrants are highlighted with the first quadrant being in the top right, the second quadrant is the top left, the bottom left quadrant is the third quadrant with the fourth quadrant being at the bottom right.
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Example 1

A four quadrant grid. A star is 2 across the x-axis and 4 up the y-axis. A circle is -3 across the x-axis and 2 up the y-axis. A square is -5 across the x-axis and -2 down the y-axis. A hexagon is  4 along the x-axis and -3 down the y-axis.

What are the coordinates of the star, the circle, the square and hexagon?

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Example 2

A four quadrant grid. Point A is within the second quadrant - coordinates (-3, 3). Point B is within the first quadrant - coordinates (1, 3). Point D is within the third quadrant - coordinates (-3, -2).

Three vertices of a rectangle have been plotted on this grid.

What are the coordinates of the missing vertex C?

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Example 3

A four quadrant grid, point A is within the second quadrant, -4 across the x axis, 3 up the y axis. Point B is within the first quadrant, 0 along the x axis, 3 along the y axis.

What are the coordinates of the line AB?

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