Can These Points Form a Square in Geometric Constructions?

[heyo12]

let ABDE and BCGH be squares lying outside the traingle ABC. The centres of these sqaures are P & Q respecitvely, and the midpoints of the line segments AC and DH are R & S respectively. Show that the points P,Q,R,S are vertices of a square?

any ideas on how to do this please?

the only hint i have is to show that P-S = R-Q = i(R -P) where i = imaginary..

 

[Chris Hillman]

Er... this is homework, correct? FYI, somewhere around PF we have a special place with special rules for homework help.

Here's a hint: if you have an equation like $z = i \, w$, you know that $z, w$ are complex numbers, yes? But you know that these can be thought of as vectors, right? So what does $z = i \, w$ mean geometrically?