If PQRS is a rhombus, then its 4 sides are equal in lengths.
So, PS = RS
Let (a,b) be the coordinates of S.
Then,
((a+3)^2 +(b -8)^2 = (a -5)^2 +(b -4))^2 -----(1)
In the line y = x+3,
b = a +3 -----------(2)
Solve those two equations simultaneously to find "a" and b.
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For the coordinates of Q:
See the relation of point P to point S.
It must be the same retion of point Q to point R.
Thus, Q is (5 +(-3 -a)),(4 +(8 -b))
Is that an AS level paper?
Anyway, the figure is a rhombus, so all its sides are equal. All you have to do is... FIRST, use the distance formula to show that is equidistant from and , or show that . SECONDLY, plug in into and show that it satisfies the equation.
I hope that helps.
me07.