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Find the number of integral points that lie exactly in the interior of the triangle with vertices (0,0) ,(0,21) ,(21,0) .

Find the number of integral points that lie exactly in the interior of the triangle with vertices (0,0) ,(0,21) ,(21,0)  .
 

Grade:12

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
The equation of the line joining (0, 21) and (21, 0) is
x+y = 21
or y = -x+21.
Thus 19, 18, ..., 0 integral points lying inside the triangle at x = 1, 2, ..., 20, respectively.
In all, there are 19+18+...+0 = 19(20)/2 = 190 points.
ankit singh
askIITians Faculty 614 Points
3 years ago

x+y=21
The number of integral solutions to the equations are x+y21, i.e., x21−y
∴ Number of integral coordinates
=19+18+....+1
=219(19+1)​=219×20​=190

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