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

: Given lines

$\begin{array}{l}2x+y=2\Rightarrow \frac{x}{1}+\frac{y}{1}=1--\left(1\right)\\ andx+y=5\Rightarrow \frac{x}{5}+\frac{y}{5}=1andx=0,y=0\end{array}$

The points lies in side the quadrilateral are (1, 1), (1, 2) ,(1,  3), (2,  1), (2,  2), (3,  1)

No of points = 6