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 (pronounced 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

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

- \(\left ( 3,0 \right )\) (Solution
- \(\left(4, 3\right)\) (Solution
- \(\left ( 3,-4 \right )\) (Solution
- \(\left ( 4,-3 \right )\) (Solution

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

- A (Solution
- C (Solution
- B (Solution
- E (Solution

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