GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
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?
[#permalink]
30 Nov 2018, 18:04
30 Nov 2018, 18:04
1
Expert Reply
5
Bookmarks
00:00
Question Stats:
75% (01:49) correct
25% (01:47) wrong based on 96 sessions
Hide Show timer Statistics
If ABCD is a square, what are the coordinates of C?
GRE exam - If ABCD is a square, what are the coordinates of C .jpg [ 12.34 KiB | Viewed 9185 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. \((\sqrt{3}, 2 \sqrt{3} )\)
Attachment:
GRE exam - If ABCD is a square, what are the coordinates of C .jpg [ 12.34 KiB | Viewed 9185 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. \((\sqrt{3}, 2 \sqrt{3} )\)
Re: If ABCD is a square, what are the coordinates of C?
[#permalink]
06 Dec 2018, 04:31
06 Dec 2018, 04:31
2
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}
AD=2
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
The ratio of sides will be 1:\sqrt{3}:2
So if we take origin O
OA=1
OB= \sqrt{3}
AD=2
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
Re: If ABCD is a square, what are the coordinates of C?
[#permalink]
30 Apr 2020, 09:24
30 Apr 2020, 09:24
1
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.
D is the answer (1+root(3)).
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.
D is the answer (1+root(3)).
