Triangle and the points

Geometry Level 3

A triangle A B C ABC has vertices with coordinates ( 0 , 0 ) (0,0) , ( 0 , 41 ) (0,41) , and ( 41 , 0 ) (41,0) .

How many points ( x , y ) (x,y) , where both x x and y y are integers, lie in the interior of △ A B C \triangle ABC ?


The answer is 780.

Mr. India by Mr. India , 17, India

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1 solution

Gandoff Tan
Aug 12, 2019

number of points = ∑ i = 1 39 i = ( 39 ) ( 39 + 1 ) 2 = ( 39 ) ( 40 ) 2 = ( 39 ) ( 20 ) = 780 \begin{aligned} \text{number of points} &=\displaystyle \sum_{i=1}^{39}i\\ &=\frac{(39)(39+1)}{2}\\ &=\frac{(39)(40)}{2}\\ &=(39)(20)\\ &=\boxed{780} \end{aligned}

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Any explanation for the formula?

Mr. India - 1 year, 9 months ago

picks theorem; A=I+B/2-1; A=840.5; l=¿; B=123/2;

ma pm - 1 year, 5 months ago

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