If a point is translated horizontally, the x-coordinate will stay the same. true or false

"horizonally" and "x-coordinate" are very much related.

If you start with a point and move the point horiz., the x-coordinate will change accordingly.  If the original point were (2,3) and the point is translated 3 units to the right, then the new x-coord. would be 2+3, or 5:  (5,3).