Cambridge IGCSE Mathematics · Syllabus 0580 · 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 IGCSE Mathematics.
Examiner tips on Coordinates
- The two Extended-only positions chain together. Sections 3.4 and 3.7 have no Core counterpart at all, and because a question may assess more than one part of the subject content, an Extended paper can build a whole multi-part question out of them — midpoint, length, gradient and perpendicular bisector, all from one pair of coordinates. That is why they are worth knowing as a single connected method rather than as four separate formulas.
Questions students ask about Coordinates
How do I tell a gradient of \(0\) from an undefined gradient? Core C3.3
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.