Question

Betsy participates in a scavenger hunt that requires her to retrieve items from four locations. The locations are on a map with the following coordinates:

Location 1 is at (−4, −1).

Location 2 is at ​​(−4, 4).

Location 3 is at (3, 4).

Location 4 is at (3, −1).

The paths from one location to another are straight lines. One unit on the coordinate grid equals 10 yards. Betsy starts at location 1 and goes to location 2, then location 3, and then location 4, and then returns back to location 1.

What is the total distance Betsy has traveled?

Answer 1

Betsy traveled a total distance of 240 yards by moving between four locations on a map, following a rectangular path where each side's distance was calculated based on the difference in coordinates.

Step-by-step explanation:

The total distance Betsy has traveled in the scavenger hunt can be calculated by finding the distances between each of the consecutive locations and adding them together. Since we are dealing with a rectangular path on the coordinate grid, the distance between each point is simply the difference in either the x-coordinates or the y-coordinates, as they form vertical and horizontal lines, respectively.

From Location 1 to Location 2, Betsy travels vertically upwards. The distance is the difference in y-coordinates: 4 - (-1) = 5 units. Since one unit equals 10 yards, this is a 50-yard distance.

Then, from Location 2 to Location 3, Betsy moves horizontally to the right. The distance is the difference in x-coordinates: 3 - (-4) = 7 units, or a 70-yard stretch.

From Location 3 to Location 4, Betsy travels vertically downwards. The distance again is in y-coordinates: 4 - (-1) = 5 units or 50 yards.

Finally, to complete the rectangle and return to Location 1 from Location 4, Betsy moves horizontally to the left: 3 - (-4) = 7 units, which is another stretch of 70 yards.

Adding up all these distances, the total path that Betsy travels is 50 + 70 + 50 + 70 = 240 yards.