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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If ABCD is a square, what are the coordinates of C?  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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If ABCD is a square, what are the coordinates of C? [#permalink]
Expert's post 00:00

Question Stats: 80% (01:25) correct 19% (01:21) wrong based on 46 sessions
If ABCD is a square, what are the coordinates of C?

Attachment: GRE exam - If ABCD is a square, what are the coordinates of C .jpg [ 12.34 KiB | Viewed 4102 times ]

A. $$(\sqrt{3}, \sqrt{3} )$$

B. $$(\sqrt{3}, 1+ \sqrt{3})$$

C. $$(2 \sqrt{3}, \sqrt{3} )$$

D. $$( 1+ \sqrt{3}, \sqrt{3} )$$

E. $$(\sqrt{3}, 2 \sqrt{3} )$$
[Reveal] Spoiler: OA

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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Intern Joined: 05 Dec 2018
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Re: If ABCD is a square, what are the coordinates of C? [#permalink]
1
KUDOS
It's 30-60-90 triangle
The ratio of sides will be 1:\sqrt{3}:2
So if we take origin O
OA=1
OB= \sqrt{3}
Draw a perpendicular from C onto x-axis, and take the intersection point E
Again we have a 30-60-90 triangle where
EC=\sqrt{3}
ED=1
Hence
OE= 1 + \sqrt{3}
EC=\sqrt{3}
Coordinates of C are ( 1+ \sqrt{3} , \sqrt{3} )
It's D Manager Joined: 04 Apr 2020
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Re: If ABCD is a square, what are the coordinates of C? [#permalink]
1
KUDOS
Since the side opposite 30 is length 1, so the hypotenuse is twice the side opposite to 30 which is 1*2 = 2.
And the side opposite 60 is root(3)/2 times the hypotenuse so 2 * root(3) / 2 = root(3).

Now, we know the square is titled at an angle so the point C is slightly to the right of bottom tip of the square. So X coordinate is greater than root(3).
Eliminate A, B and D which have root(3) as X-coordinate.

We need to check how far the X coordinate is. If the square were tilted at 45 degrees on X axis, then left half and the right half would be equivalent and the X coordinate would be twice root(3). But we know the square is tilted at a less than 45 degrees on the X axis (30 degrees given), so X coordinate is greater than root(3) and lesser than 2root(3). So eliminate option C.

Manager  Joined: 10 Feb 2020
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Re: If ABCD is a square, what are the coordinates of C? [#permalink]
Can someone explain by drawing diagram plz?
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Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!! Re: If ABCD is a square, what are the coordinates of C?   [#permalink] 14 Jun 2020, 02:56
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