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100 point,[tex}Maths question[/tex]The number of points having both co-ordinates as a integers, that lies interior of a triangle with vertices (0,0) , (0,41) and (41,0) ;a) 901b) 861c) 820d) 780-------------------Answer it with solution. |
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Answer» D 780 is U answer 4 down vote The problem can be approached by FINDING the area of the triangle in two ways: First, as A=12(412)=16812 Second, by an application of Pick's theorem A=i+b2−1 Now BOUNDARY points b can be calculated by considering that there is a single origin point (0,0) common to both cathetuses, 40 points unique to each of the two cathetuses, and 42 points along the HYPOTENUSE (inclusive of the end points where it intersects with the cathetuses). So b=1+2(40)+42=123, giving A=i+1212 Equating the two expressions for A, we get the number of INTERIOR points i=780. |
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