# Distance between two points

You can use Pythagoras on a coordinate grid. The horizontal and vertical gaps between two points make the short sides of a right-angled triangle.

Maths (school) · Part 06: Pythagoras and trigonometry · Card 2 of 9 · Last updated 2026-10-19

## Analogy

Like finding the shortcut across a park rather than walking round two edges.

## Example

**(1, 2) to (4, 6)**

Across = 3, up = 4
3^2 + 4^2 = 9 + 16 = 25
Distance = sqrt(25) = 5

## In practice

Satnavs calculate straight-line distances like this between two map positions.

## Practice

### Flashcards

- **What is the distance from (1, 2) to (4, 6)?** 5. The gaps are 3 and 4, so 9 + 16 = 25.

## Questions people ask

### How do you find the distance between two points?

Subtract the x values to get the horizontal gap and subtract the y values for the vertical gap. Square both gaps, add them, then take the square root. For (1, 2) and (4, 6), the gaps are 3 and 4, so the distance is 5.

### Does it matter which point you subtract first?

No. Because you square the gaps, a negative result becomes positive anyway. The gap from (1, 2) to (4, 6) is 3 across, and from (4, 6) back to (1, 2) is -3. Both give 9 when squared. Just keep the same order for the x values and the y values to stay consistent.

## Related concepts

- [Pythagoras' theorem](https://studyvisually.com/learn/science/maths-school/maths-school-part-6/maths-school-part-6-concept-1)
- [Coordinates](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-1)
- [Gradient](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-2)
- [y = mx + c](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-3)

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