Describe the locus of points equidistant from two fixed points A and B.
Unit 09 · Lesson 07 · Analytic Geometry, Loci & Conic Connections
Voronoi Thinking, Nearest-Point Regions & Design
Partition a region by nearest-site distance and explain boundaries as perpendicular-bisector loci.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to partition a region by nearest-site distance and explain boundaries as perpendicular-bisector loci.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Describe loci and intersections as solution sets defined by distance, coordinate, and boundary conditions.
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}(x-h)^2=4p(y-k)
Worked reasoning
Process: Translate the verbal distance condition into an equation or construction, solve or graph it, and test representative points.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: A locus is the complete set of all points satisfying a condition, not just several sample points that happen to work.
Khaemenes Academy · Open-Age Geometry
Voronoi Thinking, Nearest-Point Regions & Design
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Describe the locus of points equidistant from two intersecting lines.
Find the distance from (3,4) to the x-axis.
What condition makes a line tangent to a circle?
Define a parabola geometrically.
Why are Voronoi boundaries portions of perpendicular bisectors?