Loci
PART ONE
Describe the perpendicular bisector as a locus of points:
Describe the angle bisector as a locus of points:
Constructions
Let r, s be two lines and let A, B be two points.
Find the locus of the points equidistant from both r and s, and both A and B.
a)
About construction a) :
Describe the locus:
b.
About construction b) :
Describe the locus:
PART TWO
Describe the circumference as a locus of points:
How many circumferences pass through the three points?
Let's check your answer in the case below:
- Find the locus of points equidistant from both A and B;
- Find the locus of points equidistant from both B and C;
- Find the intersection between the loci.
Are A, B and C equidistant from this intersection? Why?
So, can you say how many circumferences pass through A, B and C at the same time? Use the definition of circumference as locus of points to explain.
how many circumferences pass through three collinear points?
How many circumferences pass through two points?
why?