Question

in this graph, what represents activation energy?
the black double - headed arrow at the transition state.
the drop between the energy in the reactants on the far left and the energy in the products on the far right.
the black arrow in the y - axis legend, indicating the direction of increasing free energy.

Explanation:

Activation energy is the minimum energy required to initiate a chemical reaction. It is represented by the energy difference between the reactants and the transition state. The black double - headed arrow at the transition state shows this energy difference. The drop between reactants and products is the change in free energy ($\Delta G$) of the reaction, not activation energy. The black arrow in the y - axis legend is just indicating the direction of increasing free energy, not activation energy.

Answer:

The black double - headed arrow at the transition state.