Introduction to Graphs:

Plot Points on a Coordinate System

This lesson introduces us to a coordinate system. There are many examples of coordinate systems, as shown above. The standard way to represent coordinate systems is on the Cartesian coordinate system. On the Cartesian coordinate plane, everything is based on two number lines, one that is horizontal (it lies flat like the horizon) and one that is vertical (it goes up and down). The horizontal axis is labeled as the x-axis and the vertical is the y-axis. When we describe a place on the plane, we describe it in terms of x and y similar to how we label cells in Excel or points on a map. The pair of numbers (x, y) that represent a point is called a coordinate and x and y are a coordinate pair. Just as x comes before y in the alphabet, x always comes before y in a coordinate point. The key is to remember that the x-value is the number that corresponds with the horizontal axis and the y-value is the number that corresponds with the vertical axis.

The following video will show how this works on a picture of a Cartesian plane.

Video Source (04:48 mins) | Transcript

Now that we know how to read a coordinate, we’re going to learn how to plot a point on a Cartesian coordinate system.

Video Source | (02:19 mins, Transcript)

A Coordinate System is any system where we can describe a location using coordinates, as shown in the lesson introduction. The Cartesian Plane is the specific coordinate system with the x and y-axes.

Remember, the x-axis is the horizontal line and the y-axis is the vertical line. Also, we label a location or point with a coordinate that has the x label first, then the y label: (x, y).

Vocabulary:

Axis (pronounced with an 'is' sound like in 'history') = singular for one axis (Example: One axis is horizontal.)

Axes (pronunced with an 'eez' sound like in 'freeze') = plural for more than one axis. (Example: Both axes are needed for the coordinate system.)

Additional Resources

Khan Academy: Introduction to the Coordinate Plane (06:47 mins; Transcript)
Khan Academy: Plotting a Point (Ordered Pair) (02:07 mins; Transcript)
Khan Academy: Points on the Coordinate Plane Examples (06:49 mins; Transcript)

Practice Problems

Use the following plot of a Cartesian coordinate system to answer this question.

For each of the following coordinate pairs, give the letter of the corresponding dot on the plot.
1. \(\left ( 3,0 \right )\)
2. \(\left(4, 3\right)\)
3. \(\left ( 3,-4 \right )\)
4. \(\left ( 4,-3 \right )\)
Use the following plot of a Cartesian coordinate system to answer this question.

For each of the following letters, give the corresponding coordinate pair.
1. A
2. C
3. B
4. E

Solutions

1. Answer: D (Written Solution)
  
  Remember, each point is written in the form (x,y), with the x-coordinate written first and the y-coordinate written second. We’ll start with the x-coordinate of (3,0). To find the location of the point (3,0) we find the vertical line that crosses at 3 on the x-axis.
  
  Next, we look at our y-coordinate of (3,0). Since the y-coordinate is a 0, we find the horizontal line that crosses the y-axis at 0.
  
  The location where these two lines intersect is the point (3,0) so the answer is D.
2. Answer: C
3. Answer: B (Written Solution)
  
  Each point is written in the form (x,y), with the x-coordinate written first and the y-coordinate written second. We’ll start with the x-coordinate of \(\left({\color{Red}3},-4 \right )\). To find the location of the point \(\left ({\color{Red}3},-4 \right )\) we find the vertical line that crosses at 3 on the x-axis.
  
  Next, we look at our y-coordinate of \(\left (3,{\color{Red} -4} \right )\). Since the y-coordinate is a \({\color{Red} -4}\), we find the horizontal line that crosses the y-axis at \({\color{Red} -4}\).
  
  The location where these two lines intersect is the point \(\left (3,-4 \right )\) so the answer is B.
4. Answer: F
1. Answer: \(\left (2,5 \right )\)
2. Answer: \(\left (-2,5 \right )\)
3. Answer: \(\left (2,-5 \right )\)
4. Answer: \(\left (-2,0 \right )\)