Question

A point $P$ moves inside a square of area $4$ sq.units such that it is nearer to point of intersection of its diagonal than any vertex. Area of region traced by $P$ is-

• A. $4$
• B. $2$
• C. $3$
• D. $1$

Answer 1

The correct option is B $2$

The locus of the point equidistance from vertex and point of intersection of the diagonals will be the perpendicular bisector of the line joining the vertex and the point of intersection of the diagonals for all four vertices respectively.

The black shaded area is the reqired area.
So required area =$(\sqrt{2}{)}^2=2$