Rekha moves 15 km in East direction,then turns towards North and moves 4 km. From here she turns towards West and travels 12 km. How far and in which direction is she from her starting point?

5 km, North-East

The correct answer is Option (2) → 5 km, North-East

1. Tracking the Movements

• Starting Point: Let the starting point be $(0, 0)$.
• Movement 1 (15 km East): She moves to the right along the x-axis.

New position: $(15, 0)$.

• Movement 2 (4 km North): She moves up along the y-axis.

New position: $(15, 4)$.

• Movement 3 (12 km West): She moves to the left (subtract from x).

New position: $(15 - 12, 4) = (3, 4)$.

2. Calculating the Distance

The distance from the starting point $(0, 0)$ to the final point $(3, 4)$ can be calculated using the Pythagorean theorem:

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$\text{Distance} = \sqrt{(3 - 0)^2 + (4 - 0)^2}$

$\text{Distance} = \sqrt{3^2 + 4^2}$

$\text{Distance} = \sqrt{9 + 16} = \sqrt{25}$

$\text{Distance} = 5 \text{ km}$

3. Determining the Direction

Since the final coordinates $(3, 4)$ are both positive:

• The positive x-value ($3$) indicates she is East of the starting point.
• The positive y-value ($4$) indicates she is North of the starting point.
• Therefore, her direction relative to the start is North-East.

Conclusion

Rekha is 5 km away from her starting point in the North-East direction.