Sally drives a mini school bus. She starts at the school gate and drives $7\text{km}$ north for her first pick-up. She then turns right and drives $10\text{km}$ picking up children along the way. She takes another right turn and drives $5\text{km}$. She then takes a final right to return to the school. How far would Sally need to drive to reach back to the school gate again?

Let's track Sally's path using Cartesian coordinates starting from the school gate at $(0,0)$:
1. **Starts at school gate $(0,0)$:** Moves $7\text{km}$ North to reach $(0,7)$.
2. Turns right (East): Drives $10\text{km}$ to reach $(10,7)$.
3. Turns right (South): Drives $5\text{km}$ to reach $(10,2)$.
4. Takes a final right turn: She is currently facing South, so turning right means she is now heading West (towards the vertical y-axis line where $x=0$).

To return directly to the school gate at $(0,0)$:

* She first drives West along the current line to reach the y-axis. The horizontal distance from $x=10$ to $x=0$ is $10\text{km}$ (bringing her to $(0,2)$).
* From $(0,2)$, she needs to drive straight South to $(0,0)$, covering a vertical distance of $2\text{km}$.

Total driving distance required to reach back to the gate = $10\text{km}+2\text{km}=12\text{km}$.