# Point of Concurrency Project

## Real Life Scenario

Gracie just moved to a new town and she plans on building a new house. The commute from her work building to her new house is important to her. Gracie wants to make sure she never runs out of gas for her car so the gas station is also important to her. Another important location for Gracie is the grocery store. Gracie wants to build her new house in the center and equidistant from her work building, the gas station, and the grocery store. The three locations are all at different points but are equidistant to Gracie’s house.

## Steps

For my graphing, I started off by using even numbers and chose random numbers for my coordinates. Then, I found the midpoint of each line. After that, I found the slopes of the lines and reciprocated the slope to make it perpendicular. Then, using the point slope formula, I plugged my midpoint coordinates in and the perpendicular slopes in for each segment. I then found the line equations for each line.

My coordinates:

A(11,13)
B(8,2)
C(2,6)
D(9.5,7.5)
E(6.5,9.5)
F(5,4)

Then, to find the Point of Concurrency (Circumcenter), I set two of the line equations equal to each other and I solved for x. Once I got x, I could get y and for my POC (Circumcenter) coordinates I got (23/3,8)

## Explanation

The point of concurrency is the circumcenter for perpendicular bisectors which best fits my scenario. The circumcenter in my scenario represents Gracie's house that is equidistant from the gas station, her office building, and the grocery store. The circumcenter's coordinates were (23/3,8). The segments used to locate the point were perpendicular bisectors.