在平面直角坐标系中,点A.B的坐标分别为(-4,2)(6,4),点P是线段AB的黄金分割点,则点P的坐标是

设P(x,y)
则:x-(-4)=0.618*(6-(-4))=6.18
x=6.18-4=2.18
y-2=0.618*(4-2)=1.236
y=1.236+2=3.236

所以:P的坐标是(2.18,3.236)

过AB的直线方程为
(y-2)/(x+4)=(4-2)/(6+4)
x-5y+14=0
|AB|=2*26^(1/2)
设P点坐标为(m,n)
-4<m<6 2<n<4 (c)
(1)|PA|/|AB|=(5^(1/2)-1)/2
4PA^2=(6-2*5^(1/2))*104
(m+4)^2+(n-2)^=26(6-2*5^(1/2)) (a)
m-5n+14=0 (b)
解（a)(b)得 n=1+5^(1/2),m=5*5^(1/2)-9
P(5*5^(1/2)-9,1+5^(1/2)0
(2)|PB|/|AB|=(5^(1/2)-2)/2
同理解到n=5-5^(1/2),m=11-5*5^(1/2)
P(11-5*5^(1/2),5-5^(1/2))