Question

The number of integral points that lie exactly inside the square formed by lines x = 0, y = 0, x = 10 and y = 10
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Answer 1

The number of integral points is 81.

Step-by-step explanation:

1. For 1 unit along the x-axis, we get 9 points exactly inside the square: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8) and (1, 9).
2. For 2 units along the x-axis, we get 9 points exactly inside the square: (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8) and (2, 9).
3. In similar way, we find 9 points for each of 3 units, 4 units, ..., 9 units along the x-axis.

Therefore total number of integral points is

= 9 × 9 = 81.