As part of their fundraising for Right To Play, the student council is having a fun-fair at lunch in the schoolyard. You will be running three events at different locations: a basketball foul-shot contest, a mini-putt course, and a dunk-tank. Your job is to locate the ticket booth so that it will be the same distance from each of the events. Describe the process you would use to determine the position of the ticket booth. Create a GeoGebra design that supports your decision.

 see below

Step-by-step explanation:

I used a coordinate graph and placed the Ticket Booth at the origin (0, 0)

Then I chose a distance of 4 (you can choose any distance) and placed the three events equidistant from the origin by using the x- and y- axis to easily determine a distance of 4 from the origin.

(0 - 4, 0) = (-4, 0)

(0 + 4, 0) = (4, 0)

(0, 0 + 4) = (0, 4)

If the booths are placed first you would need to find the equation of a circle that contains all three points and place the booth at the center.

You do this by creating a system of three equations inputting the x,y coordinates of each booth and solving for h, k, r.

Equation of a circle is: (x - h)² + (y - k)² = r²

to complete this square you have to rotate about the origin 270 degrees clockwise.