Locus and Geometric Constructions
A locus is the set of all points satisfying a given condition. Understanding loci connects to circle properties, perpendicular bisectors, and angle bisectors used in geometric constructions.
What You Need to Know
Key Concept Diagram
The locus of points equidistant from a fixed point is a circle
The locus of points equidistant from two points is the perpendicular bisector of the segment joining them
The locus of points equidistant from two lines is the angle bisector
Constructions use only a compass and straightedge without measurement
Key Vocabulary
Locus
The path or set of all points satisfying a given geometric condition
Perpendicular bisector
A line at right angles to a segment passing through its midpoint
Angle bisector
A ray that divides an angle into two equal parts
Equidistant
At equal distance from two or more reference points or lines
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the locus of all points exactly 4 cm from a fixed point P?
Question 2
What geometric object is the locus of points equidistant from points A and B?
Question 3
To bisect an angle using a compass, you create intersecting arcs to find a point on:
Key Concepts Summary
- ●The locus of points equidistant from a fixed point is a circle
- ●The locus of points equidistant from two points is the perpendicular bisector of the segment joining them
- ●The locus of points equidistant from two lines is the angle bisector
- ●Constructions use only a compass and straightedge without measurement