# Point of Concurrency

### By: Vaishnavi D.

## Real Life Scenario

Vaishnavi is in London for five days and would like to go sight seeing. She wants to go to each main attraction within three days. She wants to go see the London Eye the first day, Buckingham Palace the next day, and Big Ben the third. Vaishnavi wants to make everything out of her trip, so she wants a hotel which is equidistant from each of the tourist sights that will let her get to her destination faster. This hotel must be in the center of all these three locations.

## Pictorial Representation

## Triangle of London

## Graphing Steps

To start off my graph, I found even number coordinates to make my triangle. I then found the midpoint between each coordinate. Then I found the slopes between the two coordinates. To find the perpendicular slope, reciprocal and flip the sign. Then I plugged in my midpoint coordinates to find the line equation and used the perpendicular slope for this. I did that three times for each segment. The coordinates are:

A(4,8)

B(-6,2)

C(8,-10)

D(6,-1)

E(-1,5)

F(1,-4)

A(4,8)

B(-6,2)

C(8,-10)

D(6,-1)

E(-1,5)

F(1,-4)

## POC: (3,-5/3)

## Solution

The point of concurrency in this is the circumcenter. The coordinates of the circumcenter are (3,-5/3). This point represents the hotel in which all three tourists attractions are equidistant from. The segments that were used were perpendicular bisectors, which were represented as the roads leading from the hotel to the attractions.