# Algebraic Measure

## Algebraic Measure

Real number that expresses the distance between two points A and B of a directed line.

Therefore, an algebraic measure is a number with a sign. The sign indicates the direction in which the displacement occurs; a positive sign indicates a displacement from A to B and a negative sign indicates a displacement from B to A.

### Examples

Consider the points A and B on a directed line.

• The algebraic measure of the set of two points (A, B) is the real number k such that m(A, B) = $$k \overrightarrow {u}$$, where $$\overrightarrow {u}$$ is a unit vector.
• If m(A, B) = 10, then m(B, A) = −10.

The ratio $$\frac{5}{3}$$ of a dilation D with a centre O is the ratio of two algebraic measures.