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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Square+Coordinate Plane
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akshatgupta87
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confused mind
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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
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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akshatgupta87
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GMATGuruNY
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Step 1: If area = 100, side = 10.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 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:
Number of possible squares = 12.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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