设A、B、C、D为平面内四点,且向量AB=向量CD,A（3,1）,B（-2,2）,C（-1,4）

AB = CD
A(3,1),B(-2,2),C(-1,4)
let P (x,y)
OP = OA+ tBD
(x,y) = (3,1) + t(BC+CD)
= (3,1) + t(BC+AB)
= (3,1) + t((1,2) + (-5,1))
= (3-4t,1+3t)
x = 3-4t (1)
y = 1+3t (2)
3(1)+4(2)
3x+4y = 9+4
3x+4y = 13
P的轨迹 :3x+4y = 13