Quick Reference SheetGeometry & Trigonometry
Coordinate Geometry Quick Guide
A better quick guide to coordinate distance and slope, with sketch-first checks and subtraction-order reminders.
Filename: coordinate-geometry-quick-guide.pdfFile size: 3 KB
Formula highlights
Distance
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Slope
m = (y2 - y1) / (x2 - x1)
Core relationships
- Distance comes from Pythagorean reasoning on horizontal and vertical changes.
- Slope is rise over run.
- Vertical lines have undefined slope.
Worked examples
(1, 2) to (5, 5): distance 5, slope 3/4.
(-2, 4) to (3, -1): slope -1, matching the visual fall from left to right.
Quick reminders
- Keep subtraction order consistent in slope calculations.
- Distance is never negative.
- A sketch often reveals a sign mistake instantly.
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