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)

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 equation forming from the data is x + y $<$ 41, as we cannot count the perimeter of the triangle.

Thus,total number of cases will fall in an AP with first term 39 with cd =1 and last term =1.

Thus number of coordinates $= \frac{39 \times 40}{2} = 780$

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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:

Q. A triangle is formed by the coordinates

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Q. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0,0), (0,21)and (21,0) is

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the number of integral coordinates strictly inside triangle (integral coordinates has both x and y):

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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 (CAT 2005)

The correct option is A 780The equation forming from the data is x + y < 41, as we cannot count the perimeter of the triangle. Thus,total number of cases will fall in an AP with first term 39 with cd =1 and last term =1. Thus number of coordinates =39×402=780

The correct option is A 780
The equation forming from the data is x + y $<$ 41, as we cannot count the perimeter of the triangle.

Thus,total number of cases will fall in an AP with first term 39 with cd =1 and last term =1.

Thus number of coordinates $= \frac{39 \times 40}{2} = 780$