We have $A(0,0) B(21,0), C(0,21)$ .How to find number of points that have both coordinates integer numbers inside triangle $ABC$ ?

Question

1328 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-13T07:39:59

$(x,y)$ with $0 le x le 21$ and $0 le y le 21-x$ , with $x,y \in \mathbb{N}$

The triangle is delimited by the two axes and the line $y=-x+21$ .

So, both $x$ and $y$ range from $0$ to $21$ , and every point in the triangle lies between the line and the $x$ axis.

So, if $x=0$ , we have $y = -(0)+21$ , and so every point like

$(0,0), (0,1), ..., (0,21)$

belong to the triangle.

if $x=1$ , we have $y=-1+21=20$ , and so every point like

$(1,0), (1,1), ..., (1,20)$

So, the following points are inside the triangle:

$(x,y)$ with $0 le x le 21$ and $0 le y le 21-x$ , with $x,y \in \mathbb{N}$

We have A(0,0) B(21,0), C(0,21)A(0,0) B(21,0), C(0,21).How to find number of points that have both coordinates integer numbers inside triangle ABCABC?