## The Lesson

The Cartesian coordinates of a point can be read off from a graph.

## How to Read Off the Cartesian Coordinates of a Point

Reading off the Cartesian coordinates of a point is easy.

## Question

What are the Cartesian coordinates of the point shown on the graph below. # 1

Read off how far across the point is along the horizontal x-axis. We see that the point is 2 units along the x-axis. 2 is the x-coordinate of the point. Note: The x-axis is labelled with numbers (0, 1, 2, 3...) so you can measure how far across the point is.

# 2

Read off how far up the point is along the vertical y-axis. We see that the point is 4 units up the y-axis. 4 is the y-coordinate of the point. Note: The y-axis is labelled with numbers (0, 1, 2, 3...) so you can measure how far up the point is.

# 3

Write down the Cartesian coordinates as a pair of numbers in brackets, separated by a comma. The x-coordinate (2) found in Step 1 goes on the left. The y-coordinate (4) found in Step 2 goes on the right. ## Lesson Slides

With practice, you'll be able to read off the Cartesian coordinates of a point from by eye. The slider below gives another example of how to read off the Cartesian coordinates of a point on a graph.

## Positive and Negative Coordinates

The pair of numbers in Cartesian coordinates the can be positive and negative. • The x-axis is labelled with positive numbers to the right of the y-axis and negative numbers to the left.
• The y-axis is labelled with positive numbers above the y-axis and negative numbers below.
This means if we look at where the point is relative to the x-axis and y-axis, we can see if the x-coordinate and y-coordinate will be positive or negative. See if the point is to the left or right of the y-axis. If it is on the:
• left, the x-coordinate is negative.
• right, the x-coordinate is positive.
See if the point is above or below the x-axis. If it is:
• above, the y-coordinate is positive.
• below, the y-coordinate is negative.
Putting this together, we can see that there are four quadrants made by the two axes. Look at which quadrant a point is in to decide the sign of each coordinate.