Hint: Find the extremes of the given point by using the vertices of the triangle.
The figure for the given problem is as follows:
From the above figure it is clear that the x-coordinate of point M should lie between \[(-2,6)\], as they
are coordinates of points B and C the extremes.
Similarly, the y-coordinates of point M should lie between \[(0,3)\], as they are the coordinates of the
points A and B the extremes.
Subtracting ‘1’ from above, we get
This equation satisfies the equation (i). So, the possible values of ‘b’ are \[(0,1)\].
So, the number of integral values of \[b\]for \[M\]to lie inside the \[\Delta ABC\]is \[2\].
And the point \[M\] can be \[(0,1)\] and \[(1,2)\] .
Hence the correct answer is option (c).
Note: We can solve this by finding the equations of all the three sides then applying the condition for
two points lying on the same side. This will be a lengthy process.