Ajay takes an E-rikshaw from the bus depot and travels 8 km towards the west. Then he turns left and travels 6 km to reach his house. Given the bus stop 1 is located 12 km south of the bus depot, what is the shortest distance between Ajay's house and bus stop 1?

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**Solution:**

1. Place the bus depot at the origin point (0,0) for reference.

2. Bus stop 1 is 12 km south of the depot, so its coordinates are (0, -12).

3. Ajay travels 8 km west, so from (0,0) he moves to (-8, 0).

4. Then he turns left (which means south when facing west) and travels 6 km, reaching (-8, -6).

5. Now, find the shortest distance between Ajay's house at (-8, -6) and bus stop 1 at (0, -12).

6. Use the distance formula:
   $$	ext{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Substitute values:
   $$= \sqrt{(0 - (-8))^2 + (-12 - (-6))^2} = \sqrt{8^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 	ext{ km}$$

**Answer:** 10 km

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