To find the total distance of Alanah's trip to the arena, we need to add up the distances of each segment of her trip. We can use the distance formula to calculate the distances between the different points.
First, let's calculate the distance between Alanah's house (A) and Mia's house (M). Using the distance formula, we get:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
distance = sqrt((4 - 2)^2 + (14 - 10)^2)
distance = sqrt(4 + 16)
distance = sqrt(20)
distance ≈ 4.5
So the distance between A and M is approximately 4.5 miles.
Next, let's calculate the distance between Mia's house (M) and Teresa's house (N). Using the distance formula, we get:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
distance = sqrt((14 - 6)^2 + (16 - 12)^2)
distance = sqrt(64 + 16)
distance = sqrt(80)
distance ≈ 8.9
So the distance between M and N is approximately 8.9 miles.
Finally, let's calculate the distance between Teresa's house (N) and the arena. Using the distance formula, we get:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
distance = sqrt((16 - 10)^2 + (8 - 16)^2)
distance = sqrt(36 + 64)
distance = sqrt(100)
distance = 10
So the distance between N and the arena is exactly 10 miles.
Now we can add up the distances of the three segments to get the total distance of Alanah's trip to the arena:
total distance = 4.5 + 8.9 + 10
total distance ≈ 23.4
Therefore, the total distance of Alanah's trip to the arena is approximately 23.4 miles