The Lesson

A point can be drawn on a graph. The Cartesian coordinates of the point tell us where to draw the point on the graph. Imagine you wanted to draw a point with Cartesian coordinates (2, 4).

How to Draw a Point from Cartesian Coordinates

Drawing a point from Cartesian coordinates is easy. Cartesian coordinates have 2 numbers.

  • The number on the left (2) is called the x-coordinate. It tells you how far across the point is (in the horizontal direction) by measuring how far along the x-axis it is.
  • The number on the right (4) is called the y-coordinate. It tells you how far up the point is (in the vertical direction) by measuring how far up the y-axis it is.

Question

Draw the point with Cartesian coordinates (2, 4) on a graph.

Step-by-Step:

1

Start with a graph.

Don't forget: A graph has a pair of axes: the horizontal axis is called the x-axis and the vertical axis is called the y-axis. They meet at the origin.

2

Find the first number in the Cartesian coordinates (called the x-coordinate). In our example, the x-coordinate is 2.
(2, 4)

3

Starting from the origin, count along the x-axis until you find the x-coordinate found in Step 2 (2).

4

Find the second number in the Cartesian coordinates (called the y-coordinate). In our example, the y-coordinate is 4.
(2, 4)

5

Count up the y-axis until you find the y-coordinate found in Step 4 (4).

6

Draw the point here.

Answer:

Lesson Slides

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

Beware

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 the x-coordinate is:
  • positive, it describes a point to the right of the y-axis.
  • negative, it describes a point to the left of the y-axis.
If the y-coordinate is:
  • positive, it describes a point above the x-axis.
  • negative, it describes a point below the x-axis.
Putting this together, we can see that there are four quadrants made by the two axes. Look at the sign of each coordinate to decide which quadrant it belongs in.