A

Step 1: Understand Thomson's experiment. In this experiment, cathode rays are passed through electric and magnetic fields. The particles (ions) are deflected due to their charge-to-mass ratio (q/m).
Step 2: If the value of q/m is the same for all positive ions, this implies that the acceleration and deflection of these ions are uniform as they penetrate the electric and magnetic fields.
Step 3: When ions with the same q/m ratio strike the photographic plate, they experience the same forces and thus will feel the same acceleration. This leads them to travel in a straight path.
Step 4: Consequently, since the ions do not experience any differential deflection based on their charge-to-mass ratios, their resultant path on the photographic plate would be a straight line.
Conclusion: Therefore, if q/m is the same for all positive ions striking the photographic plate, the correct answer is that the trace would be a straight line.
Hence, the correct answer is A.