Therefore, AP = (x-x 1, y-y 1) = (-tx 1+tx2,-ty1+ty2) = t (x2-x1,y2-y.

(it is a vector, and the arrow cannot represent it. )

AP=tAB, then PB=AB-AP=( 1-t)AB.

So AP/PB=t/( 1-t)

That is, the ratio formed by P component vector AB is t/( 1-t).