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Plot Points on a Coordinate System
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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.

Plotting Points on a Coordinate System

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.

Practice Plotting Points 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

Practice Problems

1. Use the following plot of a Cartesian coordinate system to answer this question.
This is a plot of a Cartesian coordinate system that has x-axis from negative 5 to 5 and y-axis from negative 5 to 5. Point A has x equal to 3 and y equal to 4. Point B has x equal to 3 and y equal to negative 4. Point C has x equal to 4 and y equal to 3. Point D has x equal to 3 and y equal to 0. Point E has x equal to 0 and y equal to 3. Point F has x equal to 4 and y equal to negative 3. Point G has x equal to negative 3 and y equal to 4. Point H has x equal to negative 3 and y equal to negative 4.
For each of the following coordinate pairs, give the letter of the corresponding dot on the plot.
  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. We’ll start with the x-coordinate of \(({\color{Red}3},0)\). To find the location of the point \(({\color{Red}3},0)\) we find the vertical line that crosses at \({\color{Red}3}\) on the x-axis.

    A coordinate plane with a vertical line going through 3 on the x axis.

    Next, we look at our y-coordinate of \((3,{\color{Red}0})\). Since the y-coordinate is a \({\color{Red}0}\), we find the horizontal line that crosses the y-axis at \({\color{Red}0}\).

    A coordinate plane with a vertical line going through 3 on the x axis and a horizontal line passing through 0 on the y axis. There is a blue dot at the intersection of the two lines.

    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. We’ll start with the x-coordinate of \(({\color{Red}3},−4)\). To find the location of the point \(({\color{Red}3},−4)\) we find the vertical line that crosses at 3 on the x-axis.

    A coordinate plane with a vertical line that crosses the x axis at 3.

    Next, we look at our y-coordinate of \((3,{\color{Red}−4})\). Since the y-coordinate is a \({\color{Red}−4}\), we find the horizontal line that crosses the y-axis at \({\color{Red}−4}\).

    A coordinate plane with a vertical line going through 3 on the x axis and a horizontal line passing through negative 4 on the y axis. There is a blue dot at the intersection of the two lines.

    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
    )
2. Use the following plot of a Cartesian coordinate system to answer this question.
This is a plot of a Cartesian coordinate system that has x axis from negative 6 to 6 and y axis from negative 6 to 6. Point A has x equal to 2 and y equal to 5. Point B has x equal to 2 and y equal to negative 5. Point C has x equal to negative 2 and y equal to 5. Point D has x equal to negative 5 and y equal to negative 2. Point E has x equal to negative 2 and y equal to 0. Point F has x equal to 5 and y equal to negative 2. Point G has x equal to negative 5 and y equal to 2. Point H has x equal to 0 and y equal to negative 2.
For each of the following letters, give the corresponding coordinate pair.
  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:
    \((-2,0)\)
    )

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