Graphing and Locating Points

Graphing and Locating Points on the Coordinate System

University Instructors

What is a coordinate grid system?

A coordinate system is a grid system that can be used to locate any point. It is made up of two straight lines that cross each other to form a right angle. The horizontal line that runs from left to right is called the x-axis. The vertical line that runs up and down is called the y-axis.

What is a coordinate grid system? (continued)

The x-axis and the y-axis cross at a point where it is zero for each axis. That specific point is called the origin. From these lines crossing each other in this way, four sections called quadrants are created in the coordinate system.

What is a coordinate grid system? (continued)

The quadrants make it easier to locate any point on the coordinate grid. Each point on the grid is called a coordinate or an ordered pair.

What is a coordinate grid system? (continued)

The origin is shown on this grid as a black square at the point (0,0). This is always the starting point whenever you want to graph or plot a coordinate or ordered pair.

How to graph an ordered pair

When you start from the origin, the first direction that you would go would be along the x-axis. That means that you would go either left or right. The second step is to go directly up or down from the x-axis itself. Then, you will have created your ordered pair.

How to graph an ordered pair (Example 1)

For example, if you wanted to plot the ordered pair (4, 3), you would start at the origin. You would move 4 places to the right along the x-axis to end up on 4. From there, you would move 3 places up. Once you have done that, then the green circle's location is where your coordinate would be in Quadrant I (One).

How to graph an ordered pair (Example 2)

Suppose you wanted to plot the ordered pair (-3, 6). From the origin, you would move 3 places to the left along the x-axis to land on -3. From there, you would move 6 places up. Once you have done that, then the red square's location is where your coordinate would be in Quadrant II (Two).

How to graph an ordered pair (Example 3)

For graphing the ordered pair (-2, -5) where you start at the origin, you would move 2 places to the left along the x-axis to land on -2. From there, you would move 5 places down. Once you have done that, then the blue triangle's location is where your coordinate would be in Quadrant III (Three).

How to graph an ordered pair (Example 4)

If you wanted to plot the ordered pair (8, -1), you would move 8 places to the right from the origin along the x-axis to land on 8. From there, you would move 1 place down. Once you have done that, then the purple plus sign's location is where your coordinate would be in Quadrant IV (four).

How to graph an ordered pair (Example 5)

Let's say that you wanted to graph the ordered pair (4, 0). Starting from the origin, you would move 4 places to the right along the x-axis to land on 4. Given that your second part of the coordinate is zero, you do not move up or down. The white triangle's location is where your point would be on the x-axis.

How to graph an ordered pair (Example 6)

For example, if you wanted to plot the ordered pair (0, -7), you would start at the origin. Given that your first part of the ordered pair is zero, you do not move left or right from the origin. Next, you would move down 7 from the origin along the y-axis to -7. The blue triangle's location is where your point would be on the y-axis.

Conclusion/Summary

When you plot coordinates, you will go left or right along the x-axis first, then you would go up and down on or parallel to the y-axis. Therefore, when you write the ordered pair, the coordinate is written in the form (x, y). This shows x as the number of spaces that you moved left or right and y as the number of spaces that you moved up or down.