Question

P(x,y) is called a good point if x,y belongs to N. Total no. of good points lying inside the quadrilateral formed by the line 2x+y=2, x=0, y=0 and x+y=5, is equal to (a)4 (b)2 (c)10 (d)6

Answer 1

P(x,y) is a good point if  x , y ∈ N.      N = {1,2,3,4...}

The points of intersection of 2 x + y = 2 with  x = 0 and y = 0, are (0,2) and (1,0) respectively.   The points of intersection of x+y = 5 with x = 0 and y= 0 are (0, 5) and (5, 0) respectively. Join the quadrilateral.

The points that will lie within the quadrilateral (inside the border) are:
   (1, 1), (1,2) , (1, 3)...   (2, 1), (2,2),   (3,1)
So there are six of them.

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If we count the points on the boundary : with x ≠ 0 and y ≠ 0 :
        (1,4), (2,3), (3,2), (4,1)

If we see the rest of the boundary then, there are:
    (1,0), (2,0), (3,0), (4,0), (5,0), (0,2), (0,3), (0,4), (0,5)