If the vertices of a square are abcd prove that the center o

If the vertices of a square are a,b,c,d, prove that the center of the square is 1/4(a+b+c+d). It is in length.

Let us take an example of unit square whose vertices are

a(0,0),b(0,1),c(1,0),d(1,1) so that each side is 1unit

i.e, ab=bd=dc=ca=1

Now center= 1/2(b+c)= 1/2(a+d) = (1/2 , 1/2)

And 1/4(a+b+c+d) = (1/4)(2,2) = (1/2, 1/2)

Therefore clearly center =(1/4)(a+b+c+d)