Introduction

In this lesson, you will practice plotting points on Cartesian coordinate system graphs.

These videos illustrate the lesson material below. Watching the videos is optional.

• Plotting points on a coordinate system (04:48 mins) | Transcript
• Practice plotting points on a coordinate system (02:19 mins) | Transcript

Plotting Points on a Coordinate System

You are surrounded by examples of coordinate systems. For example, Figure 1 contains a map of the Holy Land. Along the top of the map there are columns that are represented by letters A–D. Down the right-hand side there are rows numbered 1–8. Coordinates combine a letter from a column and a number from a row to help you find things on a map.

• Damascus is in column D and row 1, or D1.
• Capernaum is in column C and row 3, or C3.
• Jericho is in column C and row 6, or C6.

Figure 1

Excel is another example of a coordinate system. It has columns that are represented by letters and rows that are represented by numbers. You use the same system for naming coordinates in Excel as you did with the map. If you go to Column D and Row 7, the cell is named D7.

Figure 2

The coordinate system shown below is one that you regularly use in math. It’s called the Cartesian coordinate system.

Figure 3

In the system there are two axes: the vertical axis and the horizontal axis. The right-hand side of the horizontal axis has positive numbers, while the left-hand side has negative numbers. The part of the vertical axis that is above the horizontal axis has positive numbers, while the part below the horizontal axis has negative numbers.
Note the following elements of a coordinate system as illustrated in Figure 4:

1. The center point where the two axes meet is the origin. The origin represents 0 for both axes.
2. The horizontal axis is referred to as the x-axis.
3. The vertical axis is referred to as the y-axis.

Figure 4

Note:

• Axis = singular for one axis. (Example: One axis is horizontal.)
• Axes = plural for more than one axis. (Example: Both axes are needed for the coordinate system.)

You use the numbers on the axes to describe points in the system.

Example 1
Plot the coordinate point: (1, 1). Figure 5 shows the plot at positive 1 on the x-axis and positive 1 on the y-axis.

Figure 5

It is important to note that coordinates always list the number from the x-axis first and the number from the y-axis second such as (x, y).

Example 2
Plot the following coordinate points: (-3, 2), (1, 1), (3, 1), (5, -3), (-4, -2).

The image below shows each point. All of them have the number from the x-axis listed first, followed by the number from the y-axis. Always start at the origin (0,0) when plotting points.

For example, to plot (-3, 2) start at the origin and count 3 places to the left (because negative numbers are to the left of the x-axis). Then count 2 places up. This is where you will plot the point (-3, 2).

Figure 6

Things to Remember

• In a Cartesian coordinate system, the horizontal axis is the x-axis, and the vertical axis is the y-axis.
• Label a location or point with a coordinate that has the x label first, then the y label.
• The coordinates for an ordered pair is (x, y).
• When plotting a point on the Cartesian coordinate system, always start at the origin (0, 0).

Practice Problems

 

1. \(\left ( 3,0 \right )\) (
   Solution

   x

   Solution: Answer: D
   Details:
   Remember, each point is written in the form \((x,y)\), with the x-coordinate written first and the y-coordinate written second. Start with the x-coordinate of \(({\color{green}3},0)\). To find the location of the point \(({\color{green}3},0)\) find the vertical line that crosses at \({\color{green}3}\) on the x-axis.
   
    
   
   Next, look at the y-coordinate of \((3,{\color{green}0})\). Since the y-coordinate is a \({\color{green}0}\), find the horizontal line that crosses the y-axis at \({\color{green}0}\).
   
    
   
   The location where these two lines intersect is the point \((3,0)\) so the answer is D.
   )
2. \(\left(4, 3\right)\) (
   Solution

   x

   Solution:
   Answer: C
   )
3. \(\left ( 3,-4 \right )\) (
   Solution

   x

   Solution: Answer: B
   Details:
   Each point is written in the form (x,y), with the x-coordinate written first and the y-coordinate written second. Start with the x-coordinate of \(({\color{green}3},−4)\). To find the location of the point \(({\color{green}3},−4)\) find the vertical line that crosses at 3 on the x-axis.
   
    
   
   Next, look at the y-coordinate of \((3,{\color{green}−4})\). Since the y-coordinate is a \({\color{green}−4}\), find the horizontal line that crosses the y-axis at \({\color{green}−4}\).
   
    
   
   The location where these two lines intersect is the point \((3,−4)\) so the answer is B.
   )
4. \(\left ( 4,-3 \right )\) (
   Solution

   x

   Solution:
   Answer: F
   )

 

1. A (
   Solution

   x

   Solution:
   \((2,5)\)
   )
2. C (
   Solution

   x

   Solution:
   \((-2,5)\)
   )
3. B (
   Solution

   x

   Solution:
   \((2,-5)\)
   )
4. E (
   Solution

   x

   Solution:
   \((-2,0)\)
   )