Acceleration of hinges

Four similar rods of uniform density are connected with frictionless hinges. This frame is placed on a horizontal smooth tabletop, such that its shape is a square. Vertex P is acted upon by a horizontal force in the direction of the diagonal, and due to this force it begins to move at an acceleration of aPa_P.

If the initial acceleration of the opposite vertex Q is aQ=kaPa_Q=ka_P then find k.

k is positive if Q moves away from P and k is negative if Q moves closer to P

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