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Algebra

Distance & Midpoint

Enter two points to compute the straight-line distance between them with the distance formula d = √(Δx² + Δy²), and the midpoint as the average of the coordinates. Both results are shown with intermediate steps.

Distance & Midpoint

Distance and midpoint between two points in the plane.

Try:
Answerdistance = 5, midpoint = (2.5, 4)
  1. PointsP₁(1, 2), P₂(4, 6)
  2. DifferencesΔx = 3, Δy = 4
  3. Distanced = √(Δx² + Δy²) = √(9 + 16) = 5
  4. MidpointM = ((x₁+x₂)/2, (y₁+y₂)/2) = (2.5, 4)
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Worked examples

Distance from (1, 2) to (4, 6) Use the distance formula to find the length between two points.

Key terms

Pythagorean theorem In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

Frequently asked questions

What is the distance formula?

It comes from the Pythagorean theorem: d = √((x₂ − x₁)² + (y₂ − y₁)²).

How is the midpoint found?

The midpoint is the average of the two points: ((x₁ + x₂)/2, (y₁ + y₂)/2).

Can I use negative coordinates?

Yes. Any real coordinates, positive or negative, are accepted.

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