Co-ordinate Geometry
280. Meet the Cartesian Plane · Two axes, one origin, infinite possibilities
The x-axis and y-axis always intersect at a right angle at the origin.
The Cartesian plane is formed by two perpendicular number lines — the horizontal x-axis and the vertical y-axis — meeting at the origin (0, 0). Every point is located by its pair of coordinates relative to these axes.
What this lesson covers
Try to break it
Drag P around the plane. The axes split it into four quadrants — top-right (+, +), top-left (−, +), bottom-left (−, −), bottom-right (+, −). Pull P onto an axis and one coordinate hits 0; pull it onto the origin and both do.
How you build it
Mark the origin and plot a point on the graduated plane.
- Click the centre where the horizontal x-axis and vertical y-axis cross. This is the origin O = (0, 0).
- Plot a point P anywhere on the plane. Read its address by counting along the x-axis (right or left) and the y-axis (up or down) from O.
The proof, step by step
Prove that the x-axis and y-axis meet at right angles at the origin.
- The x-axis and y-axis intersect at a single point called the Origin (O). At this point, both coordinates are zero: (0, 0).
- Any point lying exactly on the x-axis will always have a y-coordinate of 0, because it has no vertical distance from the axis.
- Any point lying exactly on the y-axis will always have an x-coordinate of 0, because it has no horizontal distance from the axis.
Worked example
What is the name of the point where the x-axis and y-axis intersect?
The point of intersection of the two axes is called the origin. It has coordinates (0, 0).
- Centroid
- Origin — correct
- Vertex
- Focus