A variable point P moving inside a sqaure whose coordinates of vertices are (1,1), (-1,-1),(-1,1) and (1,-1) in such a way that P is closer to the diagonals of sqaure compare to the coordinate axes. If A is the area of the region tranverse by P then the value of A is
Given that the point P is moving close to diagonals when compared with axes
To understand the situation, consider the movement of the point P in the first quadrant
The point P is close to diagonal means it will not move the area below the ray which makes 22.5 degrees angle with x - axis
and the point P does not move above the line which makes an angle 67.5 degrees with x - axis
The shaded region is the region where the point P moves in the first quadrant
similarly in all other quadrants too
A=4 times the above shaded region=42Area of triangle OAB−Area of triangle OAP=81211−1212−1=41−2+1=42−2=2.343A=2