Question

On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be \(\underline{\hspace{2cm}}\)

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

When dealing with movement in multiple directions, break the movements into components (horizontal and vertical), then apply the Pythagorean theorem for the total distance.

Answer 1

The Correct Option is C

To calculate the distance from point Q to point O, we will break the problem down into steps based on the movements described:

1. From point O, you travel 3 units East to point P.
2. Then, from point P, you travel 4 units South.
3. Next, you travel in the North-East direction. The North-East direction implies equal displacement along the North and East axes. After travelling North-East, you end up 6 units East of point O.
4. Finally, you travel in the North-West direction. The North-West direction also involves equal displacement along the North and West axes, and you end up 8 units North of point P.

The distances form a right-angled triangle with the horizontal and vertical components, and by using the Pythagorean theorem, we find the straight-line distance between point Q and point O is 5 units.

Final Answer: 5