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…

Let the starting point be at the origin (0, 0).

After moving 15 km East, Rekha is at position (15, 0).

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After turning North and moving 4 km, Rekha is at position (15, 4).

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After turning West and traveling 12 km, Rekha is at position:

$$(15 - 12, 4) = (3, 4)$$(15−12,4)=(3,4)

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The distance from the starting point (0, 0) to final position (3, 4) is:

$$d = \sqrt{(3-0)^2 + (4-0)^2}$$d=(3−0)2+(4−0)2​

$$d = \sqrt{9 + 16}$$d=9+16​

$$d = \sqrt{25}$$d=25​

$d = 5$d=5 km

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The final position is (3, 4), meaning Rekha is 3 km to the East and 4 km to the North of her starting point.

Therefore, she is in the North-East direction.

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

The answer is Option 2: 5 km, North-East.