The map below shows a straight local highway that runs between two towns in Massachusetts. Highway planners want to build a rest stop somewhere between the two towns.

Question

If the lead planner wants the rest stop to be 1/3 of the way from Ashton to Bedford, at what coordinates will the town be located?

Answer 1

To find the coordinates of the rest stop, we need to determine the distance between Ashton and Bedford and calculate one-third of that distance.

Let's assume that the distance between Ashton and Bedford is represented by the variable "d". The rest stop should be located one-third of "d" from Ashton.

The coordinates of Ashton can be denoted as (x1, y1), and the coordinates of Bedford can be denoted as (x2, y2). We only need to find the x-coordinate of the rest stop since the highway is described as straight.

The distance between Ashton and Bedford, "d", can be calculated using the coordinates as follows:
d = |x2 - x1|

To find one-third of the distance, we multiply "d" by 1/3:
rest stop distance = (1/3) * d

Since the rest stop is located one-third of "d" from Ashton, the x-coordinate of the rest stop can be found by adding the rest stop distance to the x-coordinate of Ashton:
rest stop x-coordinate = x1 + rest stop distance

Unfortunately, since the map and the specific coordinates of Ashton and Bedford are not provided, we cannot determine the exact coordinates of the rest stop. The calculations above provide the general methodology to find the x-coordinate of the rest stop.