First slide

Equation of line in Straight lines

Question

A lattice point in a plane is a point for which both coordinates are integers. The number of lattice points inside the triangle whose sides are
$x = 0, y = 0$ and 9x+223y=2007 is

Moderate

A

198
B

173
C

99
D

888

Solution

On the line y = 1, the number of lattice points is $[\frac{2007 - 223}{9}] = 198$
Total no of points $= \sum_{y = 1}^{8} [\frac{2007 - 223 y}{9}] = 888$

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