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)
mmmh, diagonals in a triangle ?
Label your given points A, B, and C in the corresponding order.
Clearly AB is a horizontal line, thus AB = 8
AC = √(1^2 + 9^2) = √82
BC = √(7^2 + 9^2) = √130
perimeter = 8 + √82 + √130 = appr 28.5
billy: "no" to which question?
If you mean "no, he does not have to follow the grid (that is, travel only horizontally or vertically)," then Reiny's comments (Thanks for stepping up, Reiny) solve the problem
If you mean "no, he cannot travel diagonally" then the distance traveled is the perimeter of an 8x9 rectangle.
To find the distance John traveled, we need to calculate the sum of the distances between the cities he visited. Each distance can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the cities:
1. Distance between (-4, 5) and (4, 5):
d1 = √((4 - (-4))^2 + (5 - 5)^2)
= √(8^2 + 0^2)
= √(64 + 0)
= √64
= 8
2. Distance between (4, 5) and (-3, -4):
d2 = √((-3 - 4)^2 + (-4 - 5)^2)
= √((-7)^2 + (-9)^2)
= √(49 + 81)
= √130
3. Distance between (-3, -4) and (-4, 5):
d3 = √((-4 - (-3))^2 + (5 - (-4))^2)
= √((-1)^2 + (9)^2)
= √(1 + 81)
= √82
Now, let's calculate the total distance traveled by summing up the three distances:
Total distance = d1 + d2 + d3
= 8 + √130 + √82
≈ 8 + 11.4 + 9.1
≈ 28.5
Therefore, the distance John traveled is approximately 28.5 when rounded to the nearest tenth.