Question
Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. (3 points)
Drawing a straight line from the starting point to the ending point would create a (Response area) triangle.
You can use the (Response area) to find the direct straight line distance for Jimmy.
If Jimmy took the direct line, he would have traveled approximately (Response area) meters.
Drawing a straight line from the starting point to the ending point would create a (Response area) triangle.
You can use the (Response area) to find the direct straight line distance for Jimmy.
If Jimmy took the direct line, he would have traveled approximately (Response area) meters.
Answers
GPT-4o mini
To analyze Jimmy's movement, we can visualize his route as a right triangle:
1. **Movement Breakdown**:
- Jimmy first ran 20 meters west.
- Then, he turned north and jogged 25 meters.
2. **Forming the Triangle**:
- The westward movement (20 meters) can be considered one leg of the triangle.
- The northward movement (25 meters) is the other leg.
3. **Finding the Direct Distance**:
- To find the direct distance (hypotenuse) from his starting point to his ending point, we can use the Pythagorean theorem, which states \( c^2 = a^2 + b^2 \), where:
- \( c \) is the hypotenuse (direct distance),
- \( a \) is one leg (20 meters),
- \( b \) is the other leg (25 meters).
4. **Calculating**:
- \( c^2 = 20^2 + 25^2 \)
- \( c^2 = 400 + 625 \)
- \( c^2 = 1025 \)
- \( c = \sqrt{1025} \)
- \( c \approx 32.02 \) meters.
### Responses:
- Drawing a straight line from the starting point to the ending point would create a **right triangle**.
- You can use the **Pythagorean theorem** to find the direct straight line distance for Jimmy.
- If Jimmy took the direct line, he would have traveled approximately **32.02** meters.
1. **Movement Breakdown**:
- Jimmy first ran 20 meters west.
- Then, he turned north and jogged 25 meters.
2. **Forming the Triangle**:
- The westward movement (20 meters) can be considered one leg of the triangle.
- The northward movement (25 meters) is the other leg.
3. **Finding the Direct Distance**:
- To find the direct distance (hypotenuse) from his starting point to his ending point, we can use the Pythagorean theorem, which states \( c^2 = a^2 + b^2 \), where:
- \( c \) is the hypotenuse (direct distance),
- \( a \) is one leg (20 meters),
- \( b \) is the other leg (25 meters).
4. **Calculating**:
- \( c^2 = 20^2 + 25^2 \)
- \( c^2 = 400 + 625 \)
- \( c^2 = 1025 \)
- \( c = \sqrt{1025} \)
- \( c \approx 32.02 \) meters.
### Responses:
- Drawing a straight line from the starting point to the ending point would create a **right triangle**.
- You can use the **Pythagorean theorem** to find the direct straight line distance for Jimmy.
- If Jimmy took the direct line, he would have traveled approximately **32.02** meters.