A-Level Coordinate Geometry Revision
Coordinate geometry revision for A-Level and International A-Level Maths
Coordinate geometry is where algebra and geometry meet: a circle becomes an equation, a tangent becomes a gradient condition, and a geometric fact about perpendicular lines becomes a piece of arithmetic. Most lost marks here come from forgetting the geometry — reaching for algebra when a sketch would have settled the question in a line. This free revision engine covers the coordinate geometry content of Edexcel A-Level Maths and the International A-Level Pure 1, Pure 2 and Pure 4 papers. This free revision engine covers the algebra and functions content of Edexcel A-Level Maths and the International A-Level Pure 1 to Pure 4 papers, from indices and surds in the first weeks of Year 12 through to partial fractions in Year 13. It generates a new question every time and marks your answer as you go.
What the coordinate geometry revision engine covers
Distance and midpoint — the length of a line segment, its midpoint, and dividing a segment in a given ratio Straight lines — gradients, the equation of a line through two points, parallel and perpendicular lines, and perpendicular bisectors Circles, equation and properties — the equation of a circle, finding the centre and radius by completing the square, and deciding whether a point lies inside or outside Circles, tangents and chords — the tangent at a point, the length of a tangent from an external point, and the perpendicular from the centre to a chord Parametric equations — curves defined by a parameter, finding the Cartesian equation, and differentiating parametrically
Coordinate geometry formulas you need to know
Distance between two points. The square root of the change in x squared plus the change in y squared. Midpoint. The average of the two x values and the average of the two y values. Gradient. The change in y divided by the change in x. Equation of a line. y − y₁ = m(x − x₁), using the gradient and any point on the line. Perpendicular lines. Their gradients multiply to −1, so a perpendicular gradient is −1 divided by the original. Equation of a circle. (x − a)² + (y − b)² = r², with centre (a, b) and radius r. General form. x² + y² + 2gx + 2fy + c = 0 has centre (−g, −f). Complete the square to find the radius. Circle facts worth remembering. A tangent is perpendicular to the radius at the point of contact, and the perpendicular from the centre to a chord bisects it. Tangent length. From an external point, the tangent length is √(d² − r²), where d is the distance to the centre.
How to use it
Choose a topic or an exam module. The engine generates a question and marks your answer instantly, accepting coordinates and line equations written in any equivalent form. Each question has two hints that point you at the right geometric fact rather than handing you the answer.
More A-Level Maths revision
Coordinate geometry leans heavily on algebra — completing the square for circles, and the discriminant for deciding whether a line meets a curve. If those feel shaky, the algebra revision engine is worth a session first. Track your progress across every topic on the revision hub.