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Section 1.1 Plotting Points and the Coordinate Plane

The coordinate plane is a powerful tool for visualizing mathematical concepts. In this section, we will discuss the connection between written points and their place on the plane.
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Definition 1.1.1.

The coordinate plane is shown in the image below. It has two main lines that help you navigate it. The horizontal line that goes left-to-right across the plane is called the x-axis, and the vertical line that goes up-and-down through the plane is called the y-axis.

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Sometimes, we also called these ordered pairs, since it's a pair of numbers and the order we write them in matters.

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Example 1.1.3.

Suppose we want to plot the point (3,−5). We see that the x-coordinate is 3, which means we want to move to 3 on the x-axis. From there, we see that the y-coordinate is −5, so we will go down 5 (since it's negative). Once we have done both of those moves, we land at our final destination, shown in the graph below.

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Checkpoint 1.1.4.

Plot the point (−2,0).

Answer.
Solution.

We see that the x-coordinate is −2, which means we want to move to −2 on the x-axis (which is to the left, since it is negative). From there, we see that the y-coordinate is 0, which means we actually don't need to move up or down at all. This point is on the x-axis. Once we have done both of those moves, we land at our final destination, shown in the graph below.

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Example 1.1.5.

Suppose we want to figure out the coordinates of the point plotted below:

To figure out the x-coordiante, we trace up/down to the x-axis to see what number we land at. In this case, we trace down and see that we are at −5, so that is our x-coordinate. To figure out the y-coordiante, we trace left/right to the y-axis to see what number we land at. In this case, we trace to the right and see that we are at 1, so that is our y-coordinate. Now that we have both coordinates, we can put it all together for our final answer: (−5,1).

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Checkpoint 1.1.6.

Determine the coordinates of the point plotted below:

Answer.

(3,7)

Solution.

To figure out the x-coordiante, we trace up/down to the x-axis to see what number we land at. In this case, we trace down and see that we are at 3, so that is our x-coordinate. To figure out the y-coordiante, we trace left/right to the y-axis to see what number we land at. In this case, we trace to the right and see that we are at 7, so that is our y-coordinate. Now that we have both coordinates, we can put it all together for our final answer: (3,7).