Coordinate Geometry

Find distance, midpoint, slope and the equation of a line from coordinates, with the formula shown. Try “line through (2, 3) and (6, 11)”.

Try an example:

What you can do with the Coordinate Geometry

Distance, midpoint, slope and equation of a line.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. line through (2, 3) and (6, 11)

How the Coordinate Geometry works

  1. Slope: m = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 3) ÷ (6 − 2) = 2.
  2. Use point-slope form y − y₁ = m(x − x₁) with either point.
  3. Rearrange to y = mx + c (here y = 2x − 1).

Frequently asked questions

What is the distance formula?

d = √((x₂ − x₁)² + (y₂ − y₁)²), which is the Pythagorean theorem on the coordinate plane.

How do I find perpendicular slopes?

The perpendicular slope is the negative reciprocal: if m = 2, the perpendicular slope is −½.

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