Raju started his Journey by going 4 km towards the north direction, then 3 km towards the west, and then 8 km south. How far is he from the initial point?a)6 kmb)5 kmc)7 kmd)8 kmCorrect answer is option 'B'. Can you explain this answer?

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Answer

Solution:

To find the distance between Raju's final and initial positions, we need to use Pythagoras theorem.

Let us assume that Raju's initial position is the origin, (0,0) on a 2-D coordinate plane.

Then, his final position can be plotted as follows:

- He goes 4 km towards the north, which means he moves 4 units up from the origin. His new position is (0,4).
- He goes 3 km towards the west, which means he moves 3 units to the left from his current position. His new position is (-3,4).
- He goes 8 km towards the south, which means he moves 8 units down from his current position. His final position is (-3,-4).

Thus, the distance between his final and initial positions can be calculated as follows:

Distance = √[(final x-coordinate - initial x-coordinate)² + (final y-coordinate - initial y-coordinate)²]

Distance = √[(-3 - 0)² + (-4 - 0)²]

Distance = √(9 + 16)

Distance = √25

Distance = 5 km

Therefore, Raju is 5 km away from his initial position. The correct answer is option B.

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