From his house, X went $15\text{km}$ to the north. Then he turned east and covered $10\text{km}$. Then he turned south and covered $5\text{km}$. Finally turning to the west, he covered $10\text{km}$. In which direction is he now, with respect to his house?

Let's trace X's path step by step starting from his house at origin point $O(0,0)$:
1. He goes $15\text{km}$ North to arrive at point $A(0,15)$.
2. He turns East and covers $10\text{km}$ to reach point $B(10,15)$.
3. He turns South and covers $5\text{km}$ to reach point $C(10,10)$.
4. Finally, turning West, he covers $10\text{km}$ to arrive at point $D(0,10)$.

Comparing his final location $D(0,10)$ with his initial home position $O(0,0)$, point $D$ lies directly due North along the vertical axis.