The architect's drawing uses a key where 1 cm represents 2 m. Given that the room is 9 m by 12 m, we can calculate the dimensions of the room in the drawing by scaling it down using the key.
For the length of 9 m, we divide it by 2 (since 1 cm represents 2 m) to find the corresponding measurement in the drawing. Therefore, the length in the drawing would be 4.5 cm.
Similarly, for the width of 12 m, dividing it by 2 gives us 6 cm in the drawing.
Therefore, the dimensions of the room in the drawing would be 4.5 cm by 6 cm.