Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #10

1

Parallelogram OPQR lies in the xy-plane, as shown

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2,4) and the coordinates of point Q are (8, 6). What are the coordinates of point R? (3, 2), (3, 3), (4, 4), (5, 2), (6, 2)

5 Explanations

1

Is it right to assume that PQ=OR & OP=RQ ?

Feb 5, 2020 • Comment

Yep, that's just fine! In a parallelogram, opposite sides are always equal.

1

Alaap Dhall

I used intuition. I fig out that the mid point of PQ is 8+2/2 = 10/2 = 5.
and R is greater than the midpoint is it has to have value of x>5.
only ans choice suitable was E.

Jul 8, 2019 • Comment

That works just fine here! You have to always be careful when relying on your eyes, but in the coordinate system everything is to scale. But for this problem, you're absolutely correct :)

3

I calculated the slope from P to O as 2 and knew that QR had to have the same slope as it is parallel, so then I just walked down the slope (down 2 over 1, down 2 over 1) to see what coordinates would lie on the line. The first coordinate is (7,4) and then the second coordinate is (6,2).

Oct 28, 2015 • Comment

3

SHUBHAM AWASTHI

What I did is, I joined PR and OQ. The midpoint of OQ will be (4,3) from where the diagonal PR will be passing. So P is (2,4). The middle point of PR/OQ is (4,3). By comparing P and Midpoint of PR or OQ, we can guess that R would be (6,2)
My logic is based on assumptions but it works :P

Oct 16, 2014 • Comment

Sunmeet Singh Sethi

Is the method mentioned by Shubham, correct way to solve the problem?
Even I followed the same strategy because diagonals of a parallelogram bisect each other.

You'll have to use some rough estimation to guess that R is at (6, 2) rather than (5, 2). But if you're comfortable with that guess, then this works just fine!

2

Chris Lele

Oct 8, 2012 • Comment