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How to Draw a Point from Cartesian Coordinates (Mathematics Lesson)

Drawing a Point from Cartesian Coordinates

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.

An Example Question

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

Step 2
Find the first number in the Cartesian coordinates (called the x-coordinate). In our example, the x-coordinate is 2.
(2,4)
Step 3
Starting from the origin, count along the x-axis until you find the x-coordinate found in Step 2 (2).



Step 4
Find the second number in the Cartesian coordinates (called the y-coordinate). In our example, the y-coordinate is 4.
(2,4)
Step 5
Count up the y-axis until you find the y-coordinate found in Step 4 (4).



Step 6
Draw the point here.

A Real Example of How to Draw a Point from Cartesian Coordinates

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.

Interactive Widget
Here is an interactive widget to help you learn about Cartesian (and polar) coordinates.
Interactive Test
  show
 


Here's a second test on drawing a point from Cartesian coordinates.
Here's a third test on drawing a point from Cartesian coordinates.

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.