squares, co-ordinates
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- Brent@GMATPrepNow
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This question is a knockoff of this one: https://www.beatthegmat.com/how-many-dif ... 78228.htmlvmahi7 wrote:Jessie made a square of side with 5 cm whose one vertex is at origin.The co-ordinates of the square made by Jessie are integers,how many such squares are possible..?
The only difference is that the right triangles with sides 6-8-10 are replaced with right triangles with sides 3-4-5
The answer is still 12
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For getting the answers of these question you should be Finding the points in only First Quadrant and on X-Axis as the number of points in each quadrant will be similar as other Quadrant are just the mirror images of adjacent quadrant about one of the axes.vmahi7 wrote:Jessie made a square of side with 5 cm whose one vertex is at origin.The co-ordinates of the square made by Jessie are integers,how many such squares are possible..?
With this, we realize that the answer must be a multiple of 4 therefore we Eliminate all options that are not multiple of 4
So here we look for the Integer values such that
X^2+Y^2 = 25 [Equation of Circle with radius 5 and centre at origin]
Now the famous triplet 3-4-5 comes into picture
One case when vertex is at (5,0) second when Vertex is at (3,4) and third is when the same vertex is at (4,3)
3 points multiplied by 4 as there will be 3 such points in each of the 4 Quadrants
Total points = 3x4 = 12
Answer: 12
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