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  4. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0) is

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Q. The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0, 0), (0, 21)$ and $(21, 0)$ is

VITEEEVITEEE 2013

Solution:

$x+y=21$
The number of integral solutions to the equation
$x + y < 21$, i.e., $ x < 21 - y$
image
$\therefore $ Number of integral coordinate
$= 19 + 18 + .... + 1$
$= \frac{19(19 + 1)}{2} = \frac{19 \times 20}{2} = 190$