Question

Mehak was in a whimsical mood and to reach her home from her office she took the following steps-4 steps towards north,3 steps towards east, 8steps towards south, 6steps towards west, 7steps towards north, 5 steps towards east, 6steps towards south, 4steps towards west and finally reached her home taking 3 steps towards north. the location of mehaks home with respect to her office is:
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Answer 1

Given:

Steps taken by Mehak while returning home from office:-

1. 4 steps towards north
2. 3 steps towards east
3. 8 steps towards south
4. 6 steps towards west
5. 7 steps towards north
6. 5 steps towards east
7. 6 steps towards south
8. 4 steps towards west
9. 3 steps towards north.

To find:

The location of Mehak's home with respect to her office

Solution:

• This question can be easily solved using graphical method.
• Draw the x and y axis and label them as the four cardinal directions: N(North), S(South), E(East), and W(West).
• Let 1 step of Mehak be equal to one centimetre on the graphical plane. For this problem we are assuming that all her steps are perfectly equal sized.
• Let the origin be Mehak's office. Mark it with a special symbol.
• Starting from there we will follow all the nine steps that she takes to reach her home on a daily basis.
• We will mark the direction of her movement with arrows for easy mapping and understanding.
• After the last step i.e the 9th step of her routine is followed, we would mark the end point i.e her home with a different symbol.

From the graph we can see that the distance of her Home with respect to her office is 2 steps in the west direction.

Note: If the point would have fallen between any of the four quadrants the distance would have been obtained by using Pythagoras theorem i.e $\sqrt{x^{2} +y^{2} }$ where $x$ and $y$ are values of x and y axis when point home is projected on them. And the direction with respect to office will be NE in quadrant 1, SE in quadrant 2, SW in quadrant 3 and NW in quadrant 4.