Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Coordinate Geometry
Coordinates
What is Coordinates?
An ordered pair (x, y) fixing the position of a point in a plane, measured against two perpendicular number lines: the x-coordinate gives the displacement from the origin parallel to the horizontal x-axis and is always written first, and the y-coordinate gives the displacement parallel to the vertical y-axis and is always written second. The point (0, 0) where the axes cross is the origin.
This definition is part of the Coordinate Geometry chapter in Cambridge O Level Mathematics (Syllabus D).
Questions students ask about Coordinates
How do I tell a gradient of \(0\) from an undefined gradient?
Look at which difference is zero. If the two \(y\)-coordinates are equal, the numerator is \(0\) and the gradient is \(0\) — a horizontal line \(y=k\). If the two \(x\)-coordinates are equal, the denominator is \(0\) and the gradient is undefined — a vertical line \(x=k\). Zero on top is fine; zero on the bottom is not.
What if a question gives me a diagram that is not to scale?
Then you may use it only for the information printed on it — coordinates, labels and stated facts — and never for anything you measure or judge by eye. If you need to know that two lines are perpendicular, calculate the gradients; if you need to know that two sides are equal, calculate both lengths. That is true even when the diagram is drawn accurately, because you are not told that it is.