Point of Concurrency Project

Scenario

I love music, and the 57th annual Grammy awards are coming up on February 8, 2015, and I would like to attend. Before I buy my ticket, I need to find the best place to sit. I want my seat to be equidistant from 3 of my favorite artists, Taylor Swift, Ed Sheeran, and Ella Yelich-O'Connor, who is best known as Lorde. Taylor is sitting at (-12,13), Ed is sitting at (2,17), and Ella is sitting at (11,7) Where would my seat be located?

explanation

To be an equal distance away from each of my favorite artists, I found the circumcenter of the triangle. Because the triangle is obtuse, the circumcenter is located outside of the triangle. My seat would be located at about (-2, 4 1/2) and that would make me equidistant from Taylor Swift, Ed Sheeran, and Lorde. I used arc marks to find the perpendicular bisector of all three lines, and where the lines intersected is where the circumcenter is located. By finding the perpendicular bisectors of each line, I found the circumcenter, which is where my ideal seat for the 2015 Grammy's would be.

how I came up with the points for each artist's seat

I used the birthdays of each artist to come up with points. Taylor Swift's birthday is December 13, so her point was located at (-12, 13). Ed Sheeran's birthday is February 17, so his point was located at (2, 17), and finally, Lorde's birthday is November 7, which would make her point (11, 7).