Coordinate Geometry Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about coordinate geometry for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Gradient and Equation of a Line
The gradient (slope) measures steepness: m = rise/run = (y2-y1)/(x2-x1). A positive gradient slopes upward left to right, negative slopes downward. The equation of a straight line is y = mx + c where m is the gradient and c is the y-intercept.
Key Formulas
- m = (y2 - y1) / (x2 - x1)
- y = mx + c
- y - y1 = m(x - x1)
Exam Tips
- Horizontal lines have gradient 0 (y = c)
- Vertical lines have undefined gradient (x = k)
- Use y - y1 = m(x - x1) when you know a point and the gradient
Midpoint and Distance
The midpoint of a line segment is the average of the coordinates. The distance between two points uses Pythagoras' theorem applied to coordinates.
Key Formulas
- Midpoint = ((x1+x2)/2, (y1+y2)/2)
- Distance = sqrt((x2-x1) squared + (y2-y1) squared)
Exam Tips
- The distance formula is Pythagoras in disguise
- You can verify midpoint by checking it is equidistant from both endpoints
- These formulas work in 2D; they extend naturally to 3D
Parallel and Perpendicular Lines
Parallel lines have the same gradient. Perpendicular lines have gradients that multiply to -1 (negative reciprocals). To find the perpendicular bisector of a line segment, find its midpoint and the negative reciprocal of its gradient.
Key Formulas
- Parallel: m1 = m2
- Perpendicular: m1 x m2 = -1
- Perpendicular gradient = -1/m
Exam Tips
- The negative reciprocal of 3 is -1/3, of -2/5 is 5/2
- Perpendicular bisector passes through the midpoint with perpendicular gradient
- Zero and undefined are perpendicular to each other (horizontal and vertical lines)
Line-Curve Intersections
To find where a line meets a curve, set their equations equal and solve the resulting equation. This usually gives a quadratic. The number of solutions tells you the number of intersection points. If the discriminant is zero, the line is tangent to the curve.
Key Formulas
- Set y = y: substitute line equation into curve equation
- Discriminant = b squared - 4ac
Exam Tips
- Substitute the LINEAR equation into the curve equation, not vice versa
- If discriminant > 0: two intersection points
- If discriminant = 0: line is tangent (touches curve at one point)
- If discriminant < 0: no intersection
Revision Checklist
- I understand all key concepts in coordinate geometry
- I have memorised the essential coordinate geometry formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on coordinate geometry
- I know the common mistakes to avoid in coordinate geometry questions
Frequently Asked Questions
What coordinate geometry topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers coordinate geometry across both Core and Extended tiers. Key areas include gradient and equation of a line. Key areas include midpoint and distance. Key areas include parallel and perpendicular lines.
How important is coordinate geometry in the IGCSE exam?
Coordinate Geometry is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine coordinate geometry with other topics.
What are the most common mistakes in coordinate geometry?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For coordinate geometry specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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