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Determine the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.

Mar 6, 2023

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Need help on this plz Find the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.

The number of ways of choosing three points from the grid to form an isosceles right triangle is the same as the number of lattice points that are the vertices of an isosceles right triangle. We consider the four cases for the right angle of the isosceles right triangle: The right angle is at the origin (0, 0). In this case, the other two points are at (a, 0) and (0, a), where a is a positive integer. There are a total of points of this type for n = 50. The right angle is at the point (a, a), where a is a positive integer. In this case, the other two points are at (a, 0) and (0, a). There are a total of points of this type for n = 50. The right angle is at the point (-a, a), where a is a positive integer. In this case, the other two points are at (0, a) and (-a, 0). There are a total of points of this type for n = 50. The right angle is at the point (-a, -a), where a is a positive integer. In this case, the other two points are at (0, -a) and (-a, 0). There are a total of points o…

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How many different isosceles right triangles can be formed from three dots in the grid below? Two examples are shown.Thank you in advance!