What if a coordinate is zero?

Are (0, 3) and (3, 0) both the origin?

Horizontal zero puts a point on the vertical axis; vertical zero puts it on the horizontal axis. Only (0, 0) is the origin.

In (0, 3), the horizontal value is zero. Do not move sideways from the origin; find the point three units up. It lies on the vertical axis.

In (3, 0), the vertical value is zero. Find horizontal 3 and do not move up or down. The point lies on the horizontal axis. The order of 0 and 3 changes which axis contains the point.

At (0, 0), both positions are at the reference. This is the origin where the axes meet. One zero in a pair does not by itself make a point the origin; check the other value too.

The same idea works with negatives. (0, -2) is two units below the origin on the vertical axis. (-2, 0) is two left on the horizontal axis. A zero places that direction at its reference.

Do not force an axis point into the interior of one of the four regions. Say that it lies on a boundary axis. The origin lies on both axes.

Reading zero coordinates helps you include the first row when plotting a table. Next we plot an output for input zero too. A zero input is not missing data.

Listen one paragraph at a time

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Hold on to this distinction

In (0, 2), only horizontal is zero; vertical is 2. Point to both values before naming the axis.

Change it and check

Use the three examples to compare the vertical axis, horizontal axis and origin. Try negatives with zero too.

Horizontal positionVertical position

Coordinate grid with one-unit intervals. A (0, 3). Horizontal values increase rightward and vertical values upward. On small screens you may scroll the diagram horizontally.

A (0, 3) · On the vertical axis

An axis contains points with one coordinate zero. The origin belongs to both axes. This activity does not assign a quadrant number to axis points.

Try with paper and objects

Plot (0, 2), (2, 0), (0, 0), and (0, -2). Name their axes and mark only the origin as the origin.

Check and explain another example

Check your idea 1

Where is (0, -3)?

Check your idea 2

Which point lies on both axes?

Apply it in a new setting

A drone is at (-4, 0). Which description is correct?

Write an answer yourself

Return to the explanation

Compare with a solution

(0, -2) · two numbers: horizontal, then vertical

On the vertical axis horizontal is 0; two below gives vertical −2.

Does your explanation include these ideas?

Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.

Identify which position is zero.Distinguish an axis point from the origin.Explain why the origin lies on both axes.

Continue, or pause here

Represent an input-output pair as coordinates and read between a table and its points.