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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.
Related calculators

Use the formulas in live tools.