A man is going from his office to his house. He goes 15 m due West and then 8 m due North. What is the shortest distance between starting point and end point?

Options

A. 19 m
B. 20 m
C. 18 m
D. 17 m

Answer

To find the shortest distance between the starting point and the endpoint of the man's journey, we can use the Pythagorean theorem. Here's a step-by-step solution:

### Step 1: Understand the movement
The man first moves 15 meters due West and then 8 meters due North. We can visualize this as a right triangle where:
- One leg (AB) represents the distance traveled North (8 m).
- The other leg (BC) represents the distance traveled West (15 m).

### Step 2: Identify the triangle
We can label the points:
- Point A: Starting point (office)
- Point B: After moving West (15 m)
- Point C: After moving North (8 m)

### Step 3: Apply the Pythagorean theorem
The shortest distance (AC) between the starting point and endpoint can be calculated using the Pythagorean theorem, which states:
\[ AC^2 = AB^2 + BC^2 \]
Where:
- \( AB = 8 \) m (North)
- \( BC = 15 \) m (West)

### Step 4: Substitute the values
Now substituting the values into the equation:
\[ AC^2 = 8^2 + 15^2 \]
\[ AC^2 = 64 + 225 \]

### Step 5: Calculate the sum
Now, calculate the sum:
\[ AC^2 = 289 \]

### Step 6: Find the square root
To find AC, we take the square root of both sides:
\[ AC = \sqrt{289} \]
\[ AC = 17 \, \text{m} \]

### Conclusion
The shortest distance between the starting point and the endpoint is **17 meters**.

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