Number of integral points (integral point means both coordinates should be integer) exactly in inter

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9.Straight Line

medium

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

$133$

$190$

$233$

$105$

(IIT-2003)

Solution

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

Standard 11

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medium

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hard

(JEE MAIN-2024)

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

Solution

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