解:设n个定点为(x1,y1)(x2,y2),...,(xn,yn)
设待求点为(x0,y0),则
距离平方和=(x0-x1)^2+(x0-x2)^2+,...,+(x0-xn)^2+(y0-y1)^2+(y0-y2)^2+,...,+(y0-yn)^2 =f(x0,y0)
求最小,则求偏导数。f'x(x0,y0)=2(nx0-x1-x2-,...,-xn)=0
则,x0=(x1+x2+,...,+xn)/n
同理,y0=(y1+y2+,...,+yn)/n
该点为 ((x1+x2+,...,+xn)/n, (y1+y2+,...,+yn)/n)