1.点P分有向线段AB（向量）所成的比为-1/2,可知点P在BA的延长线上,则有
令,点A坐标为(X,Y),
-3=(X-1/2*2)/(1-1/2),X=-1/2.
4=[Y-1/2*(-3)]/(1-1/2),Y=1/2.
则点A坐标为(-1/2,1/2).
2.AB/AP=入=AP/PB,
AP^2=AB*PB=AB(AB-AP),
AP^2+AB*AP-AB^2=0.
而,AB^2=(3-1)^2+(3-1)^2=8,
|AP|^2-√8*|AP|-8=0,
AP=(√10-√2).
入=|AB|/|AP|=(√5+1)/2.
令,点P坐标为(X,Y).
X=[1+(√5+1)/2*3]/[1+(√5+1)/2]=(9-√5)/2
Y=[1+(√5+1)/2*3]/[1+(√5+1)/2]=(9-√5)/2