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A cyclist goes 12 km to the South and then turning West he goes 16 km. Again he turns to his right and goes 15 km. After that, he turns to his right and goes 12 km. How far is he from his starting point?

Solution

✅ Correct Option: 3

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

The cyclist goes 12 km South:

Position: (0, -12)


The cyclist turns West and goes 16 km:

Position: (-16, -12)


The cyclist turns right (from West, right is North) and goes 15 km:

Position: (-16, -12 + 15) = (-16, 3)


The cyclist turns right (from North, right is East) and goes 12 km:

Position: (-16 + 12, 3) = (-4, 3)


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

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

d=16+9d = \sqrt{16 + 9}

d=25d = \sqrt{25}

d=5d = 5 km

Therefore, the cyclist is 5 km from the starting point.

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