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Two points and are given in the rectangular coordinate system. We want to calculate the distance between them or the length of the distance .

From the sketch, we notice that we are dealing with a right triangle, which means that we can use Pythagoras' theorem:

The distance between two points is always a non-negative number, so we use an absolute value for the length of the side of a right triangle. Hence, the two sides are written as:

Let’s use Pythagoras' theorem to calculate the hypotenuse or the length of :

Equation for the distance between two points:

The mark for distance *d* is the first letter of the Latin word *distancia*, which means distance.

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The distance between any points is always a non-negative number:

The distance between two points is equal to exactly when the points coincide:

The distance from point

*A*to point*B*is equal to the distance from point*B*to point*A*:

The distance from

*A*to*C*is less than or equal to the sum of the distances from*A*to*B*and from*B*to*C*:

The arithmetic mean of the two values *x* and *y* is equal to .

The midpoint of the line with the ends and is the point::

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material editor: Sulaiman Awwal Akinwunmi