Square+Coordinate Plane

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Square+Coordinate Plane

by akshatgupta87 » Wed Apr 13, 2011 11:34 am
Q.) 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?
A)4
B)6
C)8
D)10
E)12

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by confused mind » Wed Apr 13, 2011 12:06 pm
since area is 100 so each side=10
one vertex is at origin , so two vertices will lie on x & y axis resp and the fourth one in the quadrants ,hence 4 squares r possible

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by akshatgupta87 » Wed Apr 13, 2011 1:38 pm
Answer is E

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by GMATGuruNY » Wed Apr 13, 2011 2:06 pm
akshatgupta87 wrote:Q.) 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?
A)4
B)6
C)8
D)10
E)12
Step 1: If area = 100, side = 10.
Step 2: Recognize that the hypotenuse of a 6-8-10 triangle is 10.
Step 3: Plot coordinate pairs using every possible combination of (±6,±8), (±8,±6),(0,±10) and (±10,0).
Step 4: Using the plotted points, draw connected squares centered about the origin. Three sets of connected squares are possible:

Image

Number of possible squares = 12.

The correct answer is E.
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