Question
Shahririyar is at a winter park with his family. They go sledding located at point (2, 12) first, then ice skating located at (2, -4), then skiing located at (-8, -4). What is the total distance traveled between these locations?
Answers
GPT-4o mini
To calculate the total distance traveled by Shahririyar, we will first find the distances between each pair of locations:
1. **Distance from sledding at (2, 12) to ice skating at (2, -4)**:
The two points have the same x-coordinate (2). Therefore, the distance can be calculated using the absolute difference in the y-coordinates:
\[
\text{Distance} = |12 - (-4)| = |12 + 4| = |16| = 16
\]
2. **Distance from ice skating at (2, -4) to skiing at (-8, -4)**:
The two points have the same y-coordinate (-4). Therefore, the distance can be calculated using the absolute difference in the x-coordinates:
\[
\text{Distance} = |-8 - 2| = |-10| = 10
\]
3. **Total distance traveled**:
Now, we add the distances calculated:
\[
\text{Total Distance} = 16 + 10 = 26
\]
Therefore, the total distance traveled between these locations is \( \boxed{26} \).
1. **Distance from sledding at (2, 12) to ice skating at (2, -4)**:
The two points have the same x-coordinate (2). Therefore, the distance can be calculated using the absolute difference in the y-coordinates:
\[
\text{Distance} = |12 - (-4)| = |12 + 4| = |16| = 16
\]
2. **Distance from ice skating at (2, -4) to skiing at (-8, -4)**:
The two points have the same y-coordinate (-4). Therefore, the distance can be calculated using the absolute difference in the x-coordinates:
\[
\text{Distance} = |-8 - 2| = |-10| = 10
\]
3. **Total distance traveled**:
Now, we add the distances calculated:
\[
\text{Total Distance} = 16 + 10 = 26
\]
Therefore, the total distance traveled between these locations is \( \boxed{26} \).