Problem Solving

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


Please help me with this question.

[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