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The Perpendicular Bisector (and midpoint) of a segment with ruler and compass

Observe in the figure above how you can build, with just a ruler and a compass, the perpendicular bisector of a segment.
  1. Build it on the figure below, using the tools at the top.
  2. How would you define the perpendicular bisector of a segment? Is the line located where?
  3. Shift the ends of the initial segment and check that the construction maintains its validity.
  4. Draw a point on the perpendicular bisector and measure its distance to the two ends of the initial segment. What do all the points of the perpendicular bisector of a segment meet