Straight lines

About this lab: Straight lines

Interactive simulation for Cambridge IGCSE Mathematics 0580 topic 3 Coordinate geometry: drag two points to see the gradient as rise over run, the length of a segment by Pythagoras and its midpoint, build a line from y = mx + c, from ax + by = c or through two points with a table of values, then find parallel lines, perpendicular lines, the shortest distance to a line and the perpendicular bisector, with the working shown step by step.

IGCSE Mathematics 0580, topic 3 Coordinate geometry. Drag points on the grid: gradient, length and midpoint, the equation of a line, parallel and perpendicular lines.

Straight lines is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 3 Coordinate geometry). The course is assessed in Paper 1 (Core non-calculator), Paper 2 (Extended non-calculator), Paper 3 (Core calculator), Paper 4 (Extended calculator). Syllabus for examination in 2025-2027. There are 5 tabs, each a self-contained experiment with its own controls and live readings, and nothing to install: it runs on a laptop, tablet or classroom projector.

Syllabus coverage

• 3.1 Coordinates. Lessons: Coordinates and drawing linear graphs.
• 3.2 Drawing linear graphs. Lessons: Coordinates and drawing linear graphs.
• 3.3 Gradient of linear graphs. Lessons: Gradient of a straight line.
• 3.4 Length and midpoint (Extended). Lessons: Length and midpoint of a line segment.
• 3.5 Equations of linear graphs. Lessons: The equation of a straight line.
• 3.6 Parallel lines. Lessons: Parallel lines.
• 3.7 Perpendicular lines (Extended). Lessons: Perpendicular lines and bisectors.

Full syllabus map: IGCSE Mathematics 0580 topic 3.

How to use this simulation

1. 1. Gradient.
2. 2. Length and midpoint.
3. 3. Equation of a line.
4. 4. Parallel lines.
5. 5. Perpendicular lines.
6. The buttons at the end of the tab strip give the scene the whole window (Full screen, Hide controls) and, on a dark stage, a projector-friendly palette (Light scene). Many scenes also have drag handles: drag them to change the set-up directly.

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