Komal starts at point R and walks 8 km south to reach point S. From S, she turns left and walks 9 km to point Q. Then, she takes another left turn and walks 3 km to point T. From T, she walks 2 km east to point U. Finally, she takes a left turn and walks 3 km to point V.

Point Z is located 7 km west of point V, and point X is 5 km west of point T.

What is the distance between points Z and X?

Question

Komal starts at point R and walks 8 km south to reach point S. From S, she turns left and walks 9 km to point Q. Then, she takes another left turn and walks 3 km to point T. From T, she walks 2 km east to point U. Finally, she takes a left turn and walks 3 km to point V.

Point Z is located 7 km west of point V, and point X is 5 km west of point T.

What is the distance between points Z and X?

Accepted Answer

**Solution:**

1. Start by plotting the points step-by-step:
   - From R, Komal walks 8 km south to S.
   - From S, she turns left (which is east) and walks 9 km to Q.
   - From Q, she turns left again (now facing north) and walks 3 km to T.
   - From T, she walks 2 km east to U.
   - From U, she takes a left turn (now facing north) and walks 3 km to V.

2. Assign coordinates for clarity (taking R as origin (0,0)):
   - R = (0,0)
   - S = 8 km south of R = (0, -8)
   - Q = 9 km east of S = (9, -8)
   - T = 3 km north of Q = (9, -5)
   - U = 2 km east of T = (11, -5)
   - V = 3 km north of U = (11, -2)

3. Locate points Z and X:
   - Z is 7 km west of V: Z = (11 - 7, -2) = (4, -2)
   - X is 5 km west of T: X = (9 - 5, -5) = (4, -5)

4. Calculate the distance between Z and X:
   - Both have the same x-coordinate (4), so distance is the difference in y-coordinates:
   $$| -2 - (-5) | = | -2 + 5 | = 3 	ext{ km}$$

**Answer:** 3 km

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