Coordinate Geometry Calculator
Analyse two points at once: distance, midpoint, slope, line equation and angle.
What the Coordinate Geometry Calculator does
Coordinate geometry describes shapes using algebra. From two points you can derive everything about the line joining them: how long it is, where its centre sits, how steep it runs, and the equation that generates every other point on it.
Formula
Distance = √(Δx² + Δy²)Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2)Slope = Δy ÷ Δxy = mx + b
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| x₁ | number | Yes | — |
| y₁ | number | Yes | — |
| x₂ | number | Yes | — |
| y₂ | number | Yes | — |
How to use it
- Enter x₁, y₁, x₂ and y₂.
- Select Calculate.
Worked example
Analyse the segment from (−2, 1) to (4, 9).
- x₁, y₁
- -2, 1
- x₂, y₂
- 4, 9
Distance 10, midpoint (1, 5), slope 1.333, equation y = 1.333x + 3.667.
Reading the result
- Two points fix everything about the line through them: its length, midpoint, slope and equation.
- Parallel lines share a slope; perpendicular lines have slopes multiplying to −1.
Common mistakes
- Computing the slope as run over rise. It is the change in y divided by the change in x.
- Expecting a slope for a vertical line. The change in x is zero, so the slope is undefined rather than infinite.
Frequently asked questions
How do I tell if two lines are parallel or perpendicular?
Parallel lines have equal slopes. Perpendicular lines have slopes whose product is −1.