The number of points P(x, y) with natural num | vedclass

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(C) The quadrilateral is bounded by the lines $x = 0$ ($y$-axis),$y = 0$ ($x$-axis),$2x + y = 2$,and $x + y = 5$.For a point $(x, y)$ to be inside the

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$6$

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(C) The quadrilateral is bounded by the lines $x = 0$ ($y$-axis),$y = 0$ ($x$-axis),$2x + y = 2$,and $x + y = 5$.For a point $(x, y)$ to be inside the quadrilateral with natural number coordinates $(x \geq 1, y \geq 1)$,it must satisfy:$1) \ x + y $2) \ 2x + y > 2$Since $x, y \geq 1$,the condition $2x + y > 2$ is always satisfied for all natural numbers $(x, y)$.Now we check the condition $x + y If $x = 1$,then $1 + y If $x = 2$,then $2 + y If $x = 3$,then $3 + y If $x = 4$,then $4 + y Total points are $(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)$.There are $6$ such points.

The number of points $P(x, y)$ with natural numbers as coordinates that lie inside the quadrilateral formed by the lines $2x + y = 2$,$x = 0$,$y = 0$,and $x + y = 5$ is

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