A man goes 15 metres due west and then 8 metres due north. How far is he from the starting point?

Options

A. 19 metres
B. 16 metres
C. 17 metres
D. 15 metres

Answer

To solve the problem of how far the man is from the starting point after moving 15 meters west and then 8 meters north, 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 movement on a coordinate plane where:
- The starting point (let's call it Point A) is at the origin (0, 0).
- Moving west (left on the graph) means we subtract from the x-coordinate.
- Moving north (up on the graph) means we add to the y-coordinate.

### Step 2: Determine the Coordinates
- After moving 15 meters west, the coordinates of Point B (the position after the first movement) will be (-15, 0).
- After moving 8 meters north, the coordinates of Point C (the final position) will be (-15, 8).

### Step 3: Apply the Pythagorean Theorem
To find the distance from the starting point (Point A) to the final position (Point C), we can use the Pythagorean theorem. The distance (d) can be calculated as follows:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
- \( (x_1, y_1) \) are the coordinates of Point A (0, 0).
- \( (x_2, y_2) \) are the coordinates of Point C (-15, 8).

Substituting the values:
\[ d = \sqrt{(-15 - 0)^2 + (8 - 0)^2} \]
\[ d = \sqrt{(-15)^2 + (8)^2} \]
\[ d = \sqrt{225 + 64} \]
\[ d = \sqrt{289} \]

### Step 4: Calculate the Distance
Now we calculate the square root:
\[ d = 17 \text{ meters} \]

### Conclusion
The man is 17 meters away from the starting point.

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