[spoiler]OA : C[/spoiler]

PQRS is parallelogram, hence angle PQR can have any value

(i) equation of PR alone will not help to determine intersection of PR and QS, we need to determine point R and S. Equation of PR alone would not help

(ii) PQRS is a rectangle. Alone doesn't help

Together (i) and (ii)


- Hence we can get equation of QR (slope will be perpendicular to PQ and passes through Q.
- We can equation of RS as it will be parallel to PQ and passes through Q.
- As PQ = RS, point S can be determined.
- Once S is determined, equation of QS can be determined and also the point of intersection

The trick to this question is how you visualize the Statements. When dealing with Geometry & DS... the best trick you may apply is to Visual the answer statement on paper and judge whether you can get a rigid figure.. if you get that.. then you will definitely get answer.

You are given: P and Q coordinates..
Statement 1: you know the diagnol line but no idea of R. So you cannot draw a rigid (definite figure) INSUFFICIENT

Statement 2: you are given that PQRS is rectangle so all angles are 90 degree.. still we have no idea of height. So you cannot draw a rigid definite figure. INSUFFICIENT

Combining...
We have limiter to height of Rectangle; that's the diagnol equation.. So we get rigid Definite Figure..
Hence [spoiler]{C}[/spoiler]

kaarthikvs wrote:The Parallelogram PQRS has points P(1,6) and Q(9,12). What are the coordinates of the point of intersection of the diagonals PR and QS?
1) The equation of PR is 11y-2x=64
2) PQRS is a rectangle

Don't calculate.
DRAW.

Statement 1: The equation of PR is 11y-2x=64
y = (2/11)x + 64/11.
Don't worry about being exact.
Draw PR so that it has a POSITIVE SLOPE.

Case 1:


Case 2:


Since both cases are possible, INSUFFICIENT.

Statement 2: PQRS is a rectangle
Çase 1 also satisfies statement 2.

Case 3:


Since both cases are possible, INSUFFICIENT.

Statements combined:
Only Case 1 satisfies both statements.
Thus, the intersection of the diagonals can be determined.
SUFFICIENT.

The correct answer is C.

Thanks a lot Mitch !

If the coordinates of P (1,6) is not given in the above question then we need to find P or any other coordinates and use the below diagrammatic approach. Correct ? If so can you please let me know how we can find the coordinate P ?

Thanks a lot Mitch !

If the coordinates of P (1,6) is not given in the above question then we need to find P or any other coordinates and use the below diagrammatic approach. Correct ? If so can you please let me know how we can find the coordinate P ?

kaarthikvs wrote:Thanks a lot Mitch !

If the coordinates of P (1,6) is not given in the above question then we need to find P or any other coordinates and use the below diagrammatic approach. Correct ? If so can you please let me know how we can find the coordinate P ?

The coordinate P plays very vital role in answering this question as {C}. If we are not provided values of Coordinate then we have many cases.. two are as follows

The answer would then be {E}

i know the answer is C and it is easy to approach, but when i actually try doing this on the paper, drawing diagrams i wasnt able to do it. can someone help in doing this question for better understanding.

Good Question. IMO C. With drawing it's easy to figure it out!

opps i havnt seen micth diagrams, thanks mitch