Formulas & tables/Mathematics/Analytic geometry/Distance between two points

Distance between two points

∣AB∣=(x2−x1)2+(y2−y1)2|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Result unit: length units

What it describes

The distance between two points in the rectangular coordinate system.

Symbols

∣AB∣|AB|
distance between the points
(x1,y1),(x2,y2)(x_1,y_1),(x_2,y_2)
coordinates of the points

Where it comes from

This is the Pythagorean theorem in the coordinate system — the coordinate differences are the legs, and the distance is the hypotenuse.

When to use it

Lengths of segments, sides of polygons, radii.

Example

Given A(1,2)A(1,2), B(4,6)B(4,6). Find ∣AB∣|AB|.
SubstitutionΔx=3\Delta x=3, Δy=4\Delta y=4.
Result∣AB∣=9+16=5|AB|=\sqrt{9+16}=5.

Related formulas

Midpoint of a segment Magnitude of a vector

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