B is located 25 m south of A. C is 10 m east of B. D is 30 m north of C. E is 7 m east of D. X is 18 m south of E. M is 12 m south of X. Given that C is 7 m west of M, what is the distance between points B and M?

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**Solution:**

1. Assign coordinates to each point for clarity. Let’s place point A at the origin $(0,0)$.

2. Since B is 25 m south of A, coordinates of B are:
   $$B = (0, -25)$$

3. C is 10 m east of B, so:
   $$C = (0 + 10, -25) = (10, -25)$$

4. D is 30 m north of C:
   $$D = (10, -25 + 30) = (10, 5)$$

5. E is 7 m east of D:
   $$E = (10 + 7, 5) = (17, 5)$$

6. X is 18 m south of E:
   $$X = (17, 5 - 18) = (17, -13)$$

7. M is 12 m south of X:
   $$M = (17, -13 - 12) = (17, -25)$$

8. Given C is 7 m west of M, check if this matches coordinates:
   - C is at $(10, -25)$
   - M is at $(17, -25)$
   - Distance in x-direction between M and C is $17 - 10 = 7$ m, confirming the condition.

9. Now, find the distance between B $(0, -25)$ and M $(17, -25)$:
   - Both points lie on the same horizontal line (y = -25).
   - Distance = difference in x-coordinates = $17 - 0 = 17$ m

**Answer:** $17 	ext{ m}$

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