点A(4,3)关于X轴的对称点为A′(4,-3)
连接A′B,交X轴于点P,则PA+PB最短.
设直线A′B的解析式是y=kx+b,
将A′(4,-3),B(-2,1)代入,得
{4k+b=-3
-2k+b=1
解得:{k=-2/3
b=-1/3
∴直线A′B的解析式是y=(-2/3)x-(1/3)
令y=0,得
(-2/3)x-(1/3)=0
解得:x=-½
∴点P的坐标是(-½,0)