IP AMaths Notes (Upper Sec, Year 3-4): 06) Coordinate Geometry of Lines
Gradients, perpendicularity, and distance formula recap for line questions in IP Additional Mathematics.
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 06) Coordinate Geometry of Lines cover?
A: Gradients, perpendicularity, and distance formula recap for line questions in IP Additional Mathematics.
Linear coordinate geometry blends algebra with spatial reasoning. Track gradients and midpoints carefully and always label key coordinates on a sketch.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
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These notes align with SEAB GCE O-Level Additional Mathematics (4049) content used in IP programmes (exams from 2025).
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; still the reference for these notes.
The core idea is simple: Line geometry is gradients, distances, midpoints, and perpendicular relationships.
Use it as a working check: Sketch and label the coordinates before calculating. Most errors come from using the wrong pair of points or forgetting a negative reciprocal.
Then go one layer deeper: Example: for a perpendicular bisector, find the midpoint first, then use the negative reciprocal of the original gradient for the new line.
Choosing the right line tool
Start each coordinate-geometry question by naming the unknown: a gradient, a point, a length, or an equation. That choice determines the first calculation.
| Question cue | First tool to use | Follow-up check |
| Find the equation of a line through one point | Need a gradient first, then use point-slope form |
