Cambridge IGCSE·Mathematics 0580·Core Cartesian Coordinates

📋Key knowledge — Co Ordinate Geometry

Formulas & equations

Distance between two points: d = √((x₂−x₁)² + (y₂−y₁)²)
Midpoint: M = ((x₁+x₂)/2 , (y₁+y₂)/2)
Equation of a line through (x₁,y₁) with gradient m: y−y₁ = m(x−x₁)
Gradient: m = (y₂−y₁) ÷ (x₂−x₁)

Key facts & rules

Parallel lines: same gradient.
Perpendicular lines: gradients multiply to −1.
The equation of a circle with centre (a,b) and radius r: (x−a)² + (y−b)² = r².
A tangent to a circle is perpendicular to the radius at the point of contact.

IGCSE Co-ordinate geometry — Cartesian coordinates Practice Core

5 Cambridge IGCSE 0580 questions on cartesian coordinates at the Core tier — each with its full mark scheme. For the Extended tier on the same skill, click here.

How to approach cartesian coordinates — open the study guide

Cartesian coordinates on IGCSE 0580

Points are written as (x, y). The x-axis is horizontal, y-axis vertical. Read coordinates carefully, especially in all four quadrants where values can be negative.