Loci 4
The locus of points which are equidistant from two given points.
In plain terms:
Constructing this locus is a little bit like constructing Loci Type 3. Obviously with this loci type you are constructing a locus from two given points instead of from two given lines. You will need a compass, ruler and a pencil.
Take a look at the graphic below and the following steps to create the locus will make sense.
Draw two given points and mark them as Point A and Point B.
Draw two small arcs from Point A and two small arcs from Point B.
The 1st and 3rd Compass Marks (arcs) will form an intersect point.
The 2nd and 4th Compass Marks (arcs) will form another intersect point
Draw a line from the intersecting compass marks and this line is the Locus.
This particular Locus is a Perpendicular Bisector. This Locus is at right angles to the line joining Given Point A and Given Point B. The Locus is equidistant from both Points A and B.
You can bisect the 90 angle using the method used in Loci Type 3 to create a 45 angle without using a protractor.