For a clock with $9^{\text{th}}$ hour hand pointing towards the East, the hour hand at $1:30$ points towards which direction?

Step 1: Determine the standard direction of the $9^{\text{th}}$ hour hand.
In a normal clock layout, the $9$ o'clock position points directly to the West.

Step 2: Find the rotation shift.
According to the problem, the $9$ o'clock position points to the East. This means the directions are rotated by $180^{\circ }$ (opposite direction).

* Standard West $\to$ Shifted to East
* Standard East $\to$ Shifted to West
* Standard North $\to$ Shifted to South
* Standard South $\to$ Shifted to North

Step 3: Find the position of the hour hand at $1:30$.
At $1:30$, the hour hand is exactly halfway between $1$ and $2$. In a standard clock, the region between $12$ and $3$ (specifically $1$ and $2$) points towards the North-East.

Step 4: Rotate the standard position by $180^{\circ }$ to find the shifted direction.
The opposite direction of North-East ($\text{NE}$) is South-West ($\text{SW}$).

Therefore, the hour hand at $1:30$ points towards the South-West direction.