Consider a triangle drawn on the X - Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is:

780

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800

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820

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741

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Solution

The correct option is A 780
The formula for number of points inside a triangle is
$^{n - 1} C_{2} =^{41 - 1} C_{2} =^{40} C_{2} = \frac{40 \times 39}{2} = 20 \times 39 = 780$

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Similar questions

Q. Consider a triangle drawn on the X – Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is (CAT 2005)

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Consider a triangle drawn on the X - Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is:

The correct option is A 780The formula for number of points inside a triangle is n−1C2=41−1C2=40C2=40×392=20×39=780

The correct option is A 780
The formula for number of points inside a triangle is
$^{n - 1} C_{2} =^{41 - 1} C_{2} =^{40} C_{2} = \frac{40 \times 39}{2} = 20 \times 39 = 780$