Coordinate Geometry

Algebra meets geometry: describing lines and circles by equations, and answering geometric questions by solving them. This is DfE content area C (Coordinate geometry in the (x, y) plane).

• An Overview — the big idea, the language, the core techniques and the common mistakes

The content statements

• Straight Lines — y − y₁ = m(x − x₁), ax + by + c = 0, parallel and perpendicular lines, midpoints, distances and straight-line models
• Circles — (x − a)² + (y − b)² = r², completing the square, circle theorems in coordinates, tangents and the discriminant

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.