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

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Senior Manager
Joined: 18 Feb 2019
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If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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25 Mar 2019, 09:34
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Difficulty:

85% (hard)

Question Stats:

40% (01:42) correct 60% (01:44) wrong based on 60 sessions

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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
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Joined: 25 Mar 2019
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If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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Updated on: 26 Mar 2019, 00:43
1
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.

Originally posted by AyushmanTalukder on 25 Mar 2019, 12:16.
Last edited by AyushmanTalukder on 26 Mar 2019, 00:43, edited 1 time in total.
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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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28 Mar 2019, 10:33
How come the ans is A for this question
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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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31 Mar 2019, 13:17
kiran120680 wrote:
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

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

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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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31 Mar 2019, 16:15
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.

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If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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31 Mar 2019, 21:58
1
aaggarwal191 wrote:
How come the ans is A for this question

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
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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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04 Apr 2019, 23:25
Why cant E be to the left of A?..In that case statement 1 is insufficient..
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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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05 Apr 2019, 03:52
Debashis Roy wrote:
Why cant E be to the left of A?..In that case statement 1 is insufficient..

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.
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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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08 Apr 2019, 00:00
So Can we get such question in the actual GMAT,where the pattern is not mentioned...
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Re: If ABCD is a square in the x-y plane and the coordinates of A  [#permalink]

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08 Apr 2019, 05:15
Debashis Roy wrote:
So Can we get such question in the actual GMAT,where the pattern is not mentioned...

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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Re: If ABCD is a square in the x-y plane and the coordinates of A   [#permalink] 08 Apr 2019, 05:15
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# If ABCD is a square in the x-y plane and the coordinates of A

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