Question

Shahririyar is at a winter park with his family. They go sledding (2, 12) first, then ice skating (2, -4), then skiing (-8, -4). What is the total distance traveled between these locations?

Answer 1

To calculate the total distance traveled between the locations, we will calculate the distances between the points: sledding (2, 12), ice skating (2, -4), and skiing (-8, -4).

1. **Distance from sledding to ice skating:**
- Points: (2, 12) to (2, -4)
- The distance is calculated using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- Here, \( x_1 = 2, y_1 = 12 \) and \( x_2 = 2, y_2 = -4 \):
\[
d = \sqrt{(2 - 2)^2 + (-4 - 12)^2} = \sqrt{0 + (-16)^2} = \sqrt{256} = 16
\]

2. **Distance from ice skating to skiing:**
- Points: (2, -4) to (-8, -4)
- Similarly, we use the distance formula:
\[
d = \sqrt{(-8 - 2)^2 + (-4 - (-4))^2}
\]
- Here, \( x_1 = 2, y_1 = -4 \) and \( x_2 = -8, y_2 = -4 \):
\[
d = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10
\]

3. **Total distance traveled:**
- To find the total distance, we add the distances from step 1 and step 2:
\[
\text{Total Distance} = 16 + 10 = 26
\]

Therefore, the total distance traveled between these locations is **26** units.