1. **State the problem:** We have two points A and B, 5 cm apart, and we want to construct the locus of points equidistant from A and B. 2. **Key concept:** The locus of points equidistant from two points A and B is the perpendicular bisector of the segment AB. 3. **Steps to construct:** - Draw segment AB of length 5 cm. - Find the midpoint M of AB by measuring 2.5 cm from A towards B. - At point M, draw a line perpendicular to AB. This line is the locus of points equidistant from A and B. 4. **Explanation:** Every point on this perpendicular bisector is the same distance from A as from B because it is equidistant from both endpoints of the segment. 5. **Summary:** The locus is the perpendicular bisector of segment AB, constructed by finding the midpoint and drawing a perpendicular line through it.