Question

The number of points with integer coordinates that lie inside a triangle with coordinates $(-50,0),(50,0)$ and $(0,50)$ are
(Note: Integral coordinates means both abscissa and ordinate are integral)

• A. $2501$
• B. $2601$
• C. $2500$
• D. $2401$

Answer 1

The correct option is D $2401$

Let $(x,y)$ be the coordinates of the required point.
Therefore, $-50<x<50$ and $0<y<50$
On the line $y=k$, there are $2(49-k)+1=99-2k$ points inside the triangle.
Therefore, total number of points$=\sum _{k=1}^{49}(99-2k)=97+95+\dots +1=2401$