How to find points on a square given two points

Hi there,

I am currently in high school and was posed this problem as a challenge to solve. At first it sounded simple but i am really stuck.(Worried)

A(7,2) C(1,4)

Are the vertices on the diagonal of a sqaure ABCD, find the co-ordinates of B & D (algebraicly)

I know this can be done using vectors or just simply drawing it on the cartesian plane, however it was requested that it be done algebraicly using the perpendicular rules and other stuff like that.

Thanks