Question

Number of points with integral co-ordinates that lie inside a triangle whose co-ordinate are (0,0), (0, 21) and (21, 0)

• A. 210
• B. 190
• C. 220
• D. none of these

Answer 1

The correct option is B 190

The equation of the line joining $(0,21)$ and $(21,0)$ is

$\frac{y-0}{x-21}=\frac{21-0}{0-21}$

$x+y=21$

$\Rightarrow y=-x+21$

Thus $19,18,...,0$ integral points lying inside the triangle at $x=1,2,...,20$, respectively.

In all, there are $19+18+...+0=19\frac{20}{2}=190$ points.