Locating the Central Point Three cities (San Antonio, Houston, and Dallas) need an effective way to travel from one to another because of excessive traffic. To build a rail system they need to locate a service center that is an equal distance from all the rail lines. To find the prefect place for the service center you must find the incenter, circumcenter, orthocenter, and the centroid than determine which one is an equal distance from each line. The one closest to being the right distance away from each line and that will be the spot for the service center.
The circumcenter is a point that makes a circle that passes through each city, exactly at the city. By choosing the circumcenter would be a disadvantage because if it passes through each city than it is not close to the rail lines that only pass through the city. On the other hand if the cities were to build rail lines going through this point it would not be to out of the way from the people but could still be in the traffic parts of the rail line. An orthocenter is the connection of each attitude of the rail lines. When choosing the orthocenter it would benefit San Antonio and Houston greatly because it is so close to these two cities but is far from Dallas. Though for this rail system to work it must be equal to every rail line. The centroid is where the median of each rail line meets and is the middle of all three cities. The advantages of this is that is an even distance from the middle of the rail lines,