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

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.