Equidistant Arena

3 Act Math

Act 1

1. Where will the arena be located?
2. Write down a guess.

Credit Styling Wizard for the map.

Act 2

3. What information would be useful to figure this out?
4. Write down some questions you have in your head right now.

Here are two images to work with, one with a grid and one without.



No Grid


Possible actions include constructions, calculating the distance between points, midpoints, and writing and graphing perpendicular equations based on the information gathered.

Here is a handout with the images.

Act 3

Common Core Standards
Prove theorems about triangles.
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships
verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems


4 thoughts on “Equidistant Arena

  1. This is not exactly correct. The centroid is not always equidistant to the vertices. This would only happen in an Equilateral triangle. The three locations in this example happen to be very close to equidistant, but the way to find an equidistant location to 3 vertices is the circumcenter. This involves drawing the perpendicular bisectors (which are not always medians). I don’t mind the act three location, but the images leading up to it are deceiving. The line should start at the midpoint of the side and extend perpendicular towards the vertex. by having the line stem from the vertex it seems like the method was based on medians. Thank you for the idea however, I am going to pull my own google map of my town and create a similar scenario.

    1. Hey Evelyn,

      Thank you for the feedback! I appreciate the check. I’ll see if I can change the images leading up to act 3 in order to make it precise. A lot of these lessons need improvements so I’m thankful for your help! Hoping to get this one corrected soon.

  2. Good fix! Your new example is the circumcenter and you can verify it’s equidistance using Pythagorean’s Theorem fairly easily. The centroid of your new example would be at (6, -4 2/3) which is just slightly different than the circumcenter, so you would have to know the difference to get the correct answer. Like I said before, great problem, I did end up using my own version of this for my town. Thanks.

    1. Thanks for the quick reply! I appreciate the help. That’s awesome that you created your own. If you decide to post it online somewhere, let me know. I’d love to see how you integrated it in the classroom.

      Thanks again!

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