Homework 6920
Homework Problem 2
When the distance from B is zero, the distance from A is equal to the distance between the two cities, so we start at city B. As the distance from city B decreases and the distance from city A increases on the graph, it is represented by a straight line between A and B in the picture because the closer one gets to city A the same distance is traveled away from city B.
When the distance from city A and the distance from city B increase at the same rate, we extend the line in the picture from B to A past A until the the distance from B starts decreasing.
When the distance from B starts decreasing and the distance from A is uniform, it creates a semi circle with city A at the center.
When the distance from city A starts increasing and the distance from city B is uniform, we get another semi-circle centered at B on the picture since the distance from A increases but the distance from B is uniform.
As the distance from B decreases and the distance from A decreases, it creates a straight line from the farthest point from A on the semi-circle toward city B until the two line segments join and create one line at city B.
The difference between the two graphs is the orientation of the semi-circles. This is because there is more than one way to stay the same distance from one city and decrease (or increase) the distance from the other.