The line $3x+7y=21$ meets the co-ordinate axis at $A,B$. The rectangle $OAPB$ ($O$ being the origin) is completed. Number of lattice points in the rectangle are?
What are lattice points and how do I count them? Any help is appreciated!
Number of lattice points in a rectangle
1
$\begingroup$
geometry
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0Lattice point = point with integer coordinates. The line cuts x and y at 7 and 3 respectively, so counting the number of lattice points should be easy. Beware of fencepost errors. – 2017-02-24
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0But is there like a general formula just in case? – 2017-02-24
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1Well, $P$ is at $(7,3)$, so the number of lattice points is $(7+1)(3+1)=32$. The same idea goes for higher sizes: always add 1 to the width and height coordinates. – 2017-02-24
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0Oh yes that's true! Thanks – 2017-02-24