The diagonal of a parallelogram PQRS are along the line $x+3y=4$ and $6x-2y=7$ . Then which geometrical figure (square, rhombus, rectangle, a cyclic quadrilateral) is PQRS?
I know the slopes are perpendicular, so the diagonals are perpendicular.
I got the same question in my exam and it was under the section of multiple options correct questions. Ideally, the answer should be square, rhombus and cyclic quadrilateral. But, we can argue by saying that the condition for rhombus will always satisfy for any parallelogram while condition for square and cyclic quadrilateral will satisfy only for specific parallelogram.
So the answer should be marked as square, parallelogram and rhombus or only rhombus.