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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]

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16 Jun 2007, 21:53
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?
Director
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17 Jun 2007, 09:21
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
VP
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17 Jun 2007, 14:05
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

VP
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17 Jun 2007, 14:21
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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17 Jun 2007, 15:19
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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24 Jun 2007, 16:24
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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24 Jun 2007, 16:52
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
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