已知点A(1,4) B(3,2),向量AP=3/2向量AB,求P点的坐标

问题描述:

已知点A(1,4) B(3,2),向量AP=3/2向量AB,求P点的坐标

(4,1)

let P(x,y)
AP = (3/2)AB
OP-OA=(3/2)(OB-OA)
(x-1,y-4)=(3/2)(2,-2)=(3,-3)
=>
x-1 = 3 and y-4=-3
x=4 and y=1
P(4,1)

设P坐标是(X,Y)
向量AP=(X-1,Y-4)
向量AB=(3-1,2-4)=(2,-2)
AP=3/2AB
(X-1,Y-4)=(3,-3)
X-1=3
Y-4=-3
X=4,Y=1
即P坐标是(4,1)