If ABCD is a square in the x-y plane and the coordinates of A

Question

If ABCD is a square in the x-y plane and the coordinates of A is (2,10). Find the coordinates of E, which is the point of intersection of the diagonals.

I. The straight-line equation of line CD is y = 2.

II. Area of the square is 64 sq. unit

AyushmanTalukder · Answer

Correction : I think the coordinates of E should be (6,6).

From the given set of conditions we get a square of side length 8 units.
y=2 is a line parallel to x-axis and of length 2units. With that we get the side AC= (10-2)= 8 units.
Half of length of CD is the X-Coordinate of O, and half of AC is the Y-Coordinate of O.
ie. CD/2 = 8/2 = 4. Thus final X-Coordinate of O is (2+4) 6.
Same goes for the Y-Coordinate.

aaggarwal191 · Answer

How come the ans is A for this question

Zoom96 · Answer

Statement 1: 
This statement tells us that the the coordinates of C and D are either (2,2) and (10,2) or (-6,2) and (2,2). These two different combinations of the two coordinates C and D give us two possible E coordinates.  Insufficient

Statement 2: 
This statement doesn't tell us anything new.  Insufficient

The answer is E imo

gvij2017 · Answer

Answer of this problem is E.

St. 1 gives us two coordinates of D- (-6,2) and (10, 2).
Therefore, intersection point may lies in 1st quadrant or in 2nd quadrant as well. 
 This is insufficient.

St. 2 no other information to figure out other coordinate.

St1+St2 still gives two coordinates of D.

E is answer.

OhsostudiousMJ · Answer

1) 
Point A is given (2,10).
CD's equation is y=2. Therefore passes parallel to X-axis. And of course, is below the point A as 2 is below 10.

Now, since the equation of CD is parallel to X-axis, the side AD must be perpendicular to CD => parallel to Y-axis.

Therefore, distance is 10-2 = 8.
Length of the side = 8.
Therefore, E must be 4 points along the x axis to the right and 4 points along the y axis down. Hence, sufficient.

2)
Area of square = 64.
With A (2,10), 4 squares can be drawn with the same area, as A can be any one of the 4 vertices.
Therefore, there can be 4 E's. Hence, insufficient.

Asnwer   A

Debashis Roy · Answer

chetan2u   VeritasKarishma   Bunuel 
Why cant E be to the left of A?..In that case statement 1 is insufficient..
Please explain

KarishmaB · Answer

Yeah, I agree. Although, by norm, most figures on the co-ordinate plane have points in clockwise direction A-B-C-D, I haven't come across any such rule. So B could be to the left of A, C under B and D to the right of C.

Debashis Roy · Answer

VeritasKarishma 
So Can we get such question in the actual GMAT,where the pattern is not mentioned...

KarishmaB · Answer

Sure you can. But in that case, statement 1 alone may not be sufficient.

There is a reason GMAT has experimental questions. They weed out those questions in which they see biases. For example, if they give this as an experimental question and notice that people scoring 750 are consistently getting it wrong, they know that there is a bias somewhere. So they accordingly modify the question.

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If ABCD is a square in the x-y plane and the coordinates of A

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