If you are facing North-East and move 10 m forward, turn left and move 7.5 m, then you are

Options

A. North of your initial position
B. South of your initial position
C. East of your initial position
D. West of your initial position

Explanation

To solve the problem step by step, we will analyze the movements based on the given directions and apply the Pythagorean theorem to find the final distance from the starting point.

### Step 1: Understand the Initial Position
You are facing North-East. In terms of direction:
- North-East is a diagonal direction between North and East.

### Step 2: Move 10 m Forward
From the starting point (let's call it point A), you move 10 m in the North-East direction.
- After this movement, you reach point B.

### Step 3: Turn Left
When you are facing North-East and turn left, you will be facing North-West.
- This is because turning left from North-East means you are rotating 90 degrees anti-clockwise.

### Step 4: Move 7.5 m Forward
From point B, you move 7.5 m in the North-West direction to reach point C.

### Step 5: Visualize the Points
Now we have three points:
- Point A (starting point)
- Point B (after moving 10 m North-East)
- Point C (after moving 7.5 m North-West)

### Step 6: Determine the Right Triangle
The movement forms a right triangle (triangle ABC) where:
- AB is the hypotenuse (10 m)
- BC is one leg (7.5 m)
- AC is the other leg (the distance we want to find)

### Step 7: Apply Pythagorean Theorem
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

Substituting the known values:
- \( AB = 10 \, m \)
- \( BC = 7.5 \, m \)

So,
\[ AC^2 = (10)^2 + (7.5)^2 \]
\[ AC^2 = 100 + 56.25 \]
\[ AC^2 = 156.25 \]

### Step 8: Calculate AC
To find AC, take the square root of both sides:
\[ AC = \sqrt{156.25} \]
\[ AC = 12.5 \, m \]

### Conclusion
You are 12.5 m away from the starting point A in the direction of point C.

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