John was visiting three cities that lie on a coordinate grid at (-4, 5), (4, 5), and (-3, -4). If he visited all the cities and ended up where he started, what is the distance he traveled? Round your answer to the nearest tenth. (like 3.2 or 5.7)
Clearly, the first two points lie in a horizontal line, so the distance between them is 8
Review how to find the distance between two points given the coordinates, then find the remaining two distances.
Add up the 3 sides.
Show your work so I can check it.
To find the distance John traveled, we need to calculate the sum of the distances between each pair of consecutive cities. Let's break down the process step by step.
Step 1: Find the distance between the first city (-4, 5) and the second city (4, 5).
We can use the distance formula to calculate this:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = -4, y1 = 5, x2 = 4, and y2 = 5.
Distance = sqrt((4 - (-4))^2 + (5 - 5)^2)
Distance = sqrt((8)^2 + (0)^2)
Distance = sqrt(64 + 0)
Distance = sqrt(64)
Distance = 8
Step 2: Find the distance between the second city (4, 5) and the third city (-3, -4).
Using the same formula as above, we have:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = 4, y1 = 5, x2 = -3, and y2 = -4.
Distance = sqrt((-3 - 4)^2 + (-4 - 5)^2)
Distance = sqrt((-7)^2 + (-9)^2)
Distance = sqrt(49 + 81)
Distance = sqrt(130)
Distance ≈ 11.4
Step 3: Find the distance between the third city (-3, -4) and the first city (-4, 5).
Again, using the same formula, we have:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = -3, y1 = -4, x2 = -4, and y2 = 5.
Distance = sqrt((-4 - (-3))^2 + (5 - (-4))^2)
Distance = sqrt((-1)^2 + (9)^2)
Distance = sqrt(1 + 81)
Distance = sqrt(82)
Distance ≈ 9.1
Step 4: Find the sum of the calculated distances:
Total distance = 8 + 11.4 + 9.1
Total distance ≈ 28.5
Therefore, the distance John traveled, rounded to the nearest tenth, is approximately 28.5 units.