The formula of constant fraction point generally refers to the coordinate formula of constant fraction point of directed line segment. It is not only a common basic formula for deducing formulas, calculating and proving problems, but also a basic formula for plane geometry and analytic geometry. It plays a very wide role in geometry and can be used to solve algebraic problems.

Special case of fixed fractional point formula

Midpoint formula: two points P 1 (X 1, Y 1) and P2 (X2, Y2) are known. If the midpoint of two points is P(x, y), then x = (x1+x2)/2; Y=(y 1+y2)/2。 Triangle barycenter formula: given the triangle ABC [a (x 1, y 1), b (x2, y2), c (x3, y3)], let the triangle barycenter be G(x, y), then x = (). y=(y 1+y2+y3)/3 .