W=qv and electric potentials..

[canadianofpeace]

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Confused about the following question

Imagine a coordinate system, where point a point charge is at the origin, point Y iz 3 units above the origin and Point X is 3 units to the right of the origin. Point Z is 4 points to the right of the origin.

The question is, how does the work compare to move a charge from Z to X vs from Z to Y.

The solution manual says to use W=qV and think of it the following way

The electric potential is equal to point X or to point Y (makes sense). Therefore, the change in potential from point Z to X is the same as the change in the potential from point Z to Y, so work is equal (I don't understand this at all)...

 

[t5Nitro]

I remember this question, and it caught me off guard. If I remember right, it's because both points x and y are the same units away from the point charge, so it requires the same amount of work to move to either of those points. But this isn't my strong area.