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?
Answer & explanation
Correct answer: option 2
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.