To ascertain the boy's final distance and bearing from his residence, we will map his movement and compute the net displacement.
1. The boy's initial displacement is 6 km southward.
2. Subsequently, he moves 8 km westward.
3. His final movement is an additional 9 km southward.
This cumulative southward movement totals \(6 + 9 = 15\) km.
The boy's journey forms a right-angled triangle with legs measuring 15 km south and 8 km west.
The direct distance from his home is the hypotenuse, calculated using the Pythagorean theorem:
\[c = \sqrt{a^2 + b^2}\]
Here, \(a = 15\) km and \(b = 8\) km.
Substituting these values yields:
\[c = \sqrt{15^2 + 8^2}\]
\[c = \sqrt{225 + 64}\]
\[c = \sqrt{289}\]
\[c = 17\]
Consequently, the boy is located 17 km from his house.
Regarding his direction, given his travel south and west, his bearing from home is south-west.
Therefore, the boy is positioned 17 km South West of his origin.