A planar object made up of a uniform square plate and four semicircular discs of the same thickness and material is being acted upon by four forces of equal magnitude as shown in figure. The coordinates of point of application of forces is given by

The two forces along the y-direction balance each other.

Hence, the resultant force is 2F along the x-direction.

Let the point of application of the force be at (0, y).

(By symmetry x-coordinate will be zero).

For rotational equilibrium: 

$\begin{array}{l} \mathrm{F}\left(\mathrm{a}\right)+\mathrm{F}\left(\mathrm{a}\right)+\mathrm{F}(\mathrm{a}+\mathrm{y})-\mathrm{F}(\mathrm{a}-\mathrm{y})=0\\ \Rightarrow \mathrm{y}=-\mathrm{a}\end{array}$

Alternative method: 

Torque will only be produced by the two forces acting along y-direction in anticlockwise direction. To balance this torque, we should apply a force 2F in order to produce a torque in the clockwise direction, which is only possible if we apply a force at a point below the x-axis.