6.1: Perpendicular Bisector
This activity is intended to supplement Geometry, Chapter 5, Lesson 2.
Problem 1 – Exploring the Perpendicular Bisector Theorem
Start the Cabri Jr. application by pressing APPS and selecting CabriJr. Open the file PERBIS by pressing , selecting Open..., and selecting the file.
Line is the perpendicular bisector of . Find and using the Distance and Length tool (press GRAPH and select Measure > D.&Length). Remember that means the length of .
1. Move point to 4 different positions and record the measurements in the table below. To move the point, move the cursor over the point, press , move the point to the desired location, and then press again to release the point.
Position | position | position | position | position |
---|---|---|---|---|
2. What is the relationship between the measurements of and ?
3. Make a conjecture based on your results above about a point on the perpendicular bisector and the endpoints of a segment.
Problem 2 – An Application of the Perpendicular Bisector Theorem
John and Jane are a young college graduate couple who are relocating to a new city. They have jobs at separate locations, but work out at the same gym. They would like to buy a house that is equidistant from their jobs and gym. They use the map below and see that John’s workplace is located at , Jane’s workplace is at , and their gym is located at .
Open the Cabri Jr. file POINTS. Three points are plotted: ordered pair (1, 3.5) represents ; ordered pair (5, 3) represents ; and ordered pair (2.5, 1.5) represents .
- Use Perpendicular Bisector Theorem to decide where John and Jane should live.
- Using the map’s notation, where should the young couple live?