The fractional formula (vector P 1P=λ? Vector PP2)

Let P 1 and P2 be two points on a straight line, and p is any point on L different from P 1 and P2. Then there is a real number λ, so the vector P 1P=λ? The vector PP2, λ is called the ratio of point p to directed line segment P 1P2.

If P 1(x 1, y 1), P2(x2, y2), P(x, y), then there is

OP =(OP 1+λOP2)( 1+λ)； (Fixed Fractional Vector Formula)

x=(x 1+λx2)/( 1+λ)，

Y=(y 1+λy2)/( 1+λ). (Fixed-point coordinate formula)

Let's call the above formula the fixed point formula of the directed line segment P 1P2.