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.


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.

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