Is there any way to relate a const. line (in a 2D Sketch) to the CoG?

I am designing lifting lugs, and would like the lifting lugs to move in relation to the center of gravity (inserted via the Mass Properties window). However, when I am in the sketch and I highlight both the line or point, and the CoG feature, it does not give me any options to add a relation. Is this simply not possible or am I missing a step somewhere?

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