Straight lines, midpoints, distances and perpendicularity, applied to shapes on a grid. Nearly every question is a disguise: prove a shape is a rhombus, find where two lines meet, or turn a non-linear relationship into a straight line.
Syllabus points covered
- Find the length, gradient and midpoint of a line segment
- Find the equation of a straight line given sufficient information
- Use the relationship between gradients of parallel and perpendicular lines
- Interpret and use equations of straight lines in problems involving shapes
- Transform a given relationship to straight-line form and use the gradient and intercept
Common mistakes
- Using m₁m₂ = 1 for perpendicular lines instead of m₁m₂ = −1.
- Confusing the midpoint and gradient formulas — one adds, the other subtracts.
- In straight-line-form questions, forgetting that the gradient and intercept refer to the transformed variables, not x and y.
- Leaving an equation in a form the question didn't ask for. Read whether it wants y = mx + c or ax + by + c = 0.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Coordinate geometry with straight lines
- Coordinate geometry with straight lines — answers
- Coordinate geometry of the circle
- Coordinate geometry of the circle — answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers