Final answer:
The greatest motion between the two sides of a transform fault occurs along the horizontal or x-axis, which is prone to accumulation of stresses eventually causing earthquakes. Option number 3 is correct.
Step-by-step explanation:
The motion between the two sides of a transform fault is greatest in a lateral sense, which corresponds to the horizontal or x-axis. This is because transform faults are places where tectonic plates slide past one another horizontally. Considering the context of Earth's movements and plate tectonics, the most visible motion is along this axis, as the vertical (y-axis) movement is typically negligible and the depth (z-axis) does not represent lateral motion.
In understanding transform faults, it's also important to recognize the resulting seismic activity from these movements. Stresses build up along these faults and when released, they can cause earthquakes. The movement of the plates is typically slow and gradual, but it can accumulate significant energy over time that gets released suddenly during an earthquake.