Get coordinates of points after `Translate[]`

Suppose I have some small set of points Pts in 3D space:

Pts = Point[#] & /@ {{RandomReal[], RandomReal[],       RandomReal[]}, {RandomReal[], RandomReal[], RandomReal[]}}; 

Then, I apply Translate[] to make more points, for instance:

translatedPoints = Graphics3D@Translate[Pts, Tuples[Range[4], 3]] 

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The question is, how do I get the coordinates of the new set of points from the translatedPoints object? (as a list of points {{$ x1, y1, z1$ },..,{$ xn, yn, zn$ }})