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Coordinate geometry: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about coordinate geometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Gradient
The steepness of a line: change in y ÷ change in x.
y-intercept
Where a line crosses the y-axis: c in y = mx + c.
Parallel lines
Lines with the same gradient.
Perpendicular lines
Lines at right angles; their gradients multiply to −1.

Key formulas

Straight line: \(y=mx+c\), gradient \(m\), \(y\)-intercept \(c\); vertical line \(x=k\)
Gradient from two points\(m=\frac{y_2-y_1}{x_2-x_1}\)
Midpoint; length\(\left(\tfrac{x_1+x_2}2,\tfrac{y_1+y_2}2\right),\) \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Parallel lines\(m_1=m_2\)
Perpendicular lines\(m_1\times m_2=-1\)

Worked example

Find the equation of the line through (1, 2) and (3, 8).

  1. m = (8 − 2)/(3 − 1) = 3
  2. y = 3x + c through (1, 2): 2 = 3 + c, so c = −1

Answer: y = 3x − 1

Common mistakes

  • Gradient worked out as change in x over change in y
  • Using the same gradient for a perpendicular line instead of the negative reciprocal

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

  • Plot points in all four quadrants and draw straight-line graphs from equations by completing a table of values.
  • Find the gradient of a straight line from its graph and from the coordinates of two points on it.
  • Interpret and find equations of straight lines in the forms y = mx + c and x = k from graphs and descriptions.
  • Calculate the length and the midpoint of a line segment from the coordinates of its end points.
  • Use the fact that parallel lines have equal gradients to find the equation of a line parallel to a given line through a given point.
  • Use the gradient rule m₁ × m₂ = −1 to find equations of perpendicular lines and of the perpendicular bisector of a line segment.

The printable sheet

Coordinate geometry knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes
Coordinate geometry knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Geometry · Mensuration · Trigonometry · Transformations and vectors · Probability · Statistics · All Cambridge IGCSE Maths (0580) organisers