The number of points, having both co-ordinates as integers, that lie in the interior of th…

Question

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0, 0)$  $(0, 41)$ and $(41, 0)$ is :

Accepted Answer

The number of integral points lie inside the triangle are

1. If x = 1, then y may be 1, 2, 3, ....., 39

2. If x = 2, then y may be 1, 2, 3, ....., 38

3. If x = 3, then y may be 1, 2, 3, ....., 37

$$ \vdots $$

39. If x = 39, then the value of y is 1.

Hence, the number of interior points are
$$1 + 2 + 3 + .... + 39 = {{39 \times 40} \over 2} = 780$$

Solutions · 1