Answer the questions based on the information given below. Seven hockey players H, I, J, K, L, M & N are at different positions with each other in a hockey ground. N is 14m west of K who is 10m west of H. J is east of N. The distance between H and N is twice the distance between J and N. L is 16m north of J. M is 12m east of L. M is 10m north of I. What is the shortest distance between J and H?

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Accepted Answer

**Solution:**

1. Let's set a reference point for easier calculation. Assume H is at coordinate $(0,0)$.

2. Since K is 10 m west of H, K's position is $(-10, 0)$.

3. N is 14 m west of K, so N's position is $(-10 - 14, 0) = (-24, 0)$.

4. The distance between H and N is $|0 - (-24)| = 24$ m.

5. Given that the distance between H and N is twice the distance between J and N, so:
   $$HN = 2 	imes JN \ 24 = 2 	imes JN \ JN = 12 	ext{ m}$$

6. J is east of N, so J lies on the east side of N along the horizontal axis. Therefore, J's x-coordinate is $-24 + 12 = -12$, and y-coordinate is $0$ (same horizontal line as N).

7. L is 16 m north of J, so L's coordinates are $(-12, 16)$.

8. M is 12 m east of L, so M's coordinates are $(-12 + 12, 16) = (0, 16)$.

9. M is 10 m north of I, so I's coordinates are $(0, 16 - 10) = (0, 6)$.

10. We need to find the shortest distance between J and H:
    - H is at $(0, 0)$
    - J is at $(-12, 0)$

11. Distance between H and J:
    $$HJ = 	ext{distance between } (0,0) 	ext{ and } (-12,0) = |0 - (-12)| = 12 	ext{ m}$$

**Answer:** $12 	ext{ m}$

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