Question

the two opposite vertices if a square are (-1,2) and (3,2) .find the coordinates of the other two vertices

Answer 1

let others two opposite sides are (x, y) and (r, u)
because square is also a parellelogram so diagonal midpoint of opposite side is same.
x+r=-1+3
x+r=2------(1)
and
y+u=2+2=4 --------(2)
also square all side length same
(x-3)^2+(y-2)^2=(x+1)^2+(y-2)^2-------(3)
(r-3)^2+(u-2)^2=(r+1)^2+(u-2)^2 --------(4)
solve all equation and find it