I've got it.
First before reviewing the statements 1 and 2, we can know that Diagonals of rectangle are equal and bisect each other
=> OP=OS=OQ=OR=QS/2=6
Statement 1: Gives us no new information as it is in the given QS passes through the origin and since O is the midpoint of QS then PR MUST pass thru O and O be its midpoint as diagonals of rectangle bisect each other.
Statement 2: Angle PQS=30 => Triangle SPQ is 30:60:90 triangle
=> SP=SQ/2=6
We already new before that OP=OS=6
Therefore, now we have OP=OS=SP=6
To simplify calculation and since we want to calculate coordinates of P we can say,
OP^2=SP^2 (x=x-coordinate of P, y=y-coordinate of P)
=> y^2 + x^2 = y^2 + (x+6)^2
=> x^2 = x^2+12x+36 (eliminate x^2)
=> 12x+36=0
=> x= -36/12 = -3 and y= 36 - x^2=36-9= 27 => y= 3sqrt(3)
Therefore, P [-3,3sqrt(3) ]
So, the answer is B.
Thanks for not helping guys. But I dont know if I face it in the exam i can eliminate A easily, but you need to know the approach to take to check if B is useful or go for D instead.
Thanks hope it was useful.
