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.
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?
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.
To find the coordinates of the rest stop, we need the coordinates of both Ashton and Bedford. Unfortunately, the map is not provided, so we cannot directly determine the exact coordinates. However, we can still explain the general concept of finding the coordinates.
Coordinates on a map typically use the Cartesian coordinate system, with an x-coordinate (horizontal) and a y-coordinate (vertical). The precise coordinates depend on the scale of the map and the reference point used.
Step 1: Determine the distance between Ashton and Bedford
To find the rest stop located 1/3 of the way from Ashton to Bedford, we need to know the distance between the two towns. This distance can be measured by calculating the number of miles or using any other appropriate unit of distance.
Step 2: Divide the distance by 3
Since the rest stop is intended to be 1/3 of the way from Ashton to Bedford, divide the total distance by 3 to determine one-third of that distance.
Step 3: Add the coordinates of Ashton to one-third of the distance
To find the coordinates of the rest stop, add one-third of the distance to the x-coordinate and y-coordinate of Ashton. This will give you an estimate of where the rest stop might be located on the highway.
Without specific values or a map, I'm sorry that I cannot provide the exact coordinates. I recommend referring to a map or using a mapping tool to locate Ashton and Bedford and calculate their coordinates accurately.
To find the coordinates of the rest stop, we first need to determine the distance between Ashton and Bedford. Since the rest stop is intended to be 1/3 of the way from Ashton to Bedford, we can divide the total distance by 3.
Unfortunately, you haven't provided the map or any specific distances. However, I can still explain how you could find the coordinates of the rest stop using a general method.
1. Determine the total distance between Ashton and Bedford on the local highway. This information should be available on the map you mentioned. Let's call this total distance 'd'.
2. Divide the total distance by 3 to find the distance from Ashton to the rest stop. Let's call this distance 'd1'. So, d1 = d/3.
3. Starting from Ashton, measure or calculate the distance 'd1' along the local highway towards Bedford.
4. Once you have traveled the distance 'd1', note the spot where you are and record the coordinates.
Please refer to the map or any specific data you have to obtain the values of 'd' and the coordinates of Ashton and Bedford. With that information, you can calculate the coordinates of the rest stop by following the steps above.