Exercise 1 — Cambridge IGCSE 0580 Mar 2023 Paper 42 Q9
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Cambridge IGCSE·Mathematics 0580·Extended
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 Extended
4 Cambridge IGCSE 0580 questions on cartesian coordinates at the Extended tier — each with its full mark scheme. For the Core 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.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Jun 2023 Paper 21 Q21
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Exercise 3 — Cambridge IGCSE 0580 Jun 2023 Paper 41 Q6
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Exercise 4 — Cambridge IGCSE 0580 Nov 2023 Paper 42 Q9
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