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How to Read Off the Cartesian Coordinates of a Point (Mathematics Lesson)

Reading Off the Cartesian Coordinates of a Point

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

How to Read Off the Cartesian Coordinates a Point

Reading off the Cartesian coordinates of a point is easy.

An Example Question

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



Step 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.

Step 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.

Step 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.

A Real Example of How to Read Off the Cartesian Coordinates of a Point

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.

Interactive Widget
Here is an interactive widget to help you learn about Cartesian (and polar) coordinates.
Interactive Test
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Here's a second test on reading off the Cartesian coordinates of a point.
Here's a third test on reading off the Cartesian coordinates of a point.

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.