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:

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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