Question 898389: points P(5,1), Q(0,6) and R(-5,1) are plotted on a coordinate plane. Where must point S be located so that the quadrilateral PQRS is a square?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! PR is obviously a horizontal line (P and R have the same y=1), and is one diagonal of the square.
Its length is 10=5-(-5), the difference in the x coordinates of P and R.
The other diagonal must be a vertical line passing through Q(0,6).
That other diagonal must be also 10 units long.
Since Q(0,6) is above the diagonal PR (its y=6 is greater than the y=1 for P and R),
S must be directly below Q, 10 units down.
For S, x=0, just like for Q,
and y=6-10=-4.
So the missing vertex of the square is S(0,-4).
See the square in blue, with its diagonals in green. 
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