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The number o-f integral points (integral point means both the coordinates should be integer) exactlyin the interior of the triangle with vertices (0,0),(0,21) and (21,0) is

Chokkalingam , 5 Years ago
Grade 12th pass
anser 1 Answers
Arun

Last Activity: 5 Years ago

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.

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