Idealisation

P is treated as a single point (zero size, drawn bigger only so it's easy to grab). Grid lines are equal arbitrary units — a real measurement would carry units like m or cm.

Linked representations

Try this (optional)

Drag P so its distance from the x-axis is 5, and its distance from the y-axis is 2.

Conclusion

The x-coordinate is the perpendicular distance from the y-axis. The y-coordinate is the perpendicular distance from the x-axis. The sign just tells you which side of the axis you're on — the distance itself is always the absolute value.

Check your understanding

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coordinates-2d