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6.1: Perpendicular Bisector

Difficulty Level: At Grade Created by: CK-12
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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 \begin{align*}Y=\end{align*}Y=, selecting Open..., and selecting the file.

Line \begin{align*}CD\end{align*}CD is the perpendicular bisector of \begin{align*}\overline{AB}\end{align*}AB¯¯¯¯¯¯¯¯. Find \begin{align*}AC\end{align*}AC and \begin{align*}BC\end{align*}BC using the Distance and Length tool (press GRAPH and select Measure > D.&Length). Remember that \begin{align*}AC\end{align*}AC means the length of \begin{align*}\overline{AC}\end{align*}AC¯¯¯¯¯¯¯¯.

1. Move point \begin{align*}C\end{align*}C to 4 different positions and record the measurements in the table below. To move the point, move the cursor over the point, press \begin{align*}a\end{align*}a, move the point to the desired location, and then press \begin{align*}a\end{align*}a again to release the point.

Position \begin{align*}1^{st}\end{align*}1st position \begin{align*}2^{nd}\end{align*}2nd position \begin{align*}3^{rd}\end{align*}3rd position \begin{align*}4^{th}\end{align*}4th position

2. What is the relationship between the measurements of \begin{align*}AC\end{align*} and \begin{align*}BC\end{align*}?

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 \begin{align*}B7\end{align*}, Jane’s workplace is at \begin{align*}J6\end{align*}, and their gym is located at \begin{align*}E3\end{align*}.

Open the Cabri Jr. file POINTS. Three points are plotted: ordered pair (1, 3.5) represents \begin{align*}B7\end{align*}; ordered pair (5, 3) represents \begin{align*}J6\end{align*}; and ordered pair (2.5, 1.5) represents \begin{align*}E3\end{align*}.

  1. Use Perpendicular Bisector Theorem to decide where John and Jane should live.
  2. Using the map’s notation, where should the young couple live?

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