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#?

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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}#