In order to find the number of points inside the given triangle with integer coordinates, we can use the Pick`s theorem. Pick`s theorem states that the area of a polygon with lattice points on its boundary can be calculated using the formula:

A = B/2 + I - 1

where A is the area of the polygon, B is the number of lattice points on the boundary, and I is the number of lattice points inside the polygon.

In this case, the triangle has three vertices with integer coordinates: (0,0), (0,100), and (100,100). The length of the base of the triangle is 100 and the height is 100, so the area of the triangle is (1/2)*100*100 = 5000.

Now, let`s count the number of lattice points on the boundary of the triangle. We can see that there are 101 lattice points on the base and 101 lattice points on the left side of the triangle. However, the top side of the triangle does not have any lattice points. Therefore, the total number of lattice points on the boundary is 101+101 = 202.

Substituting the values into Pick`s theorem, we get:

5000 = 202/2 +