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If you have time, you can try this problem!

 

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

 

 Feb 12, 2023
 #1
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The grid consists of 49 points, arranged in 7 columns and 7 rows.

To form an isosceles right triangle, two of the three points must lie on the same vertical or horizontal line, and the third point must be the midpoint of the line segment connecting the other two points.

For each column and each row, there are two possible line segments connecting two points and the number of such line segments is 7 + 7 = 14.

For each line segment, there is one midpoint, so there are 14 possible midpoints.

Therefore, the number of ways of choosing three points from the grid to form an isosceles right triangle is 14 * 2 = 28.

 Feb 12, 2023

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