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A boy travels 5 km towards the South and then turns left and travels 5 km. After that, he turns to his right and walks 7 km. How far is he from the starting point finally?

Solution

✅ Correct Option: 3

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

The boy travels 5 km towards the South.

Position: (0, -5)


He turns left (which means he now faces East) and travels 5 km.

Position: (0 + 5, -5)

Position: (5, -5)


He turns to his right (which means he now faces South) and walks 7 km.

Position: (5, -5 - 7)

Position: (5, -12)


The distance from the starting point (0, 0) to the final position (5, -12) is:

d=(5−0)2+(−12−0)2d = \sqrt{(5-0)^2 + (-12-0)^2}

d=25+144d = \sqrt{25 + 144}

d=169d = \sqrt{169}

d=13d = 13

Therefore, the boy is 13 km from the starting point.

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