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A certain square is to be drawn on a coordinate plane. One

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Senior Manager
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A certain square is to be drawn on a coordinate plane. One [#permalink] New post 16 Jun 2007, 20:53
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
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 [#permalink] New post 17 Jun 2007, 08:21
12 ways the square can be drawn.
there will be three squares in each quadrant with the vertices other than origin - (10,0), (0,10), (10,10) -- 1
(6,8), (-8,6) , (-2,14) --2
(8,6), (-6,8), (2,14) --3
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 [#permalink] New post 17 Jun 2007, 13:05
I figured 4 ways

(0,0) - (0,10) - (10,0) - (10,10) = 100

(0,0) - (10,0) - (0,-10) - (-10,-10) = 100

(0,0) - (0,-10) - (10,0) - (10,10) = 100

(0,0) - (0,-10) - (-10,0) - (-10,-10) = 100


:-D
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Re: coordinate plane [#permalink] New post 17 Jun 2007, 13:21
ArvGMAT wrote:
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?


I would guess 8 ways total, but I am not sure

Set the the lower right vertex of the square to be (a,b) we know that for quadrant 1 and 2,
a^2 + b^2 = 100

Possible integers for (a,b): (10,0), (8,6), (6,8), (0,10)

Therefore, 4 quadrants would give 8.
I don't know how to check the other points...
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 [#permalink] New post 17 Jun 2007, 14:19
vshaunak@gmail.com wrote:
12 ways the square can be drawn.
there will be three squares in each quadrant with the vertices other than origin - (10,0), (0,10), (10,10) -- 1
(6,8), (-8,6) , (-2,14) --2
(8,6), (-6,8), (2,14) --3


12:

I: (10, 0), (8, 6), and (6, 8)
I: (0, 10), (-6, 8), and (-8, 6)
I: (-10, 0), (-8, -6), and (-6, -8)
I: (-10, 0), (8, -6), and (6, -8)
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 [#permalink] New post 24 Jun 2007, 15:24
OA is 8.
here are the combos -
10,0
0,10
-10,0
0,-10
6,8
-8,-6
-6,8
-8,6
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 [#permalink] New post 24 Jun 2007, 15:52
ArvGMAT,

Would you give an example as how a square is formed using the below numbers. Thank you

6,8
-8,-6
-6,8
-8,6
  [#permalink] 24 Jun 2007, 15:52
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