C

Step 1: Use the mirror formula: \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \)
Step 2: Identify object distance (u) as -30 cm (conventionally negative).
Step 3: Identify image distance (v) as -10 cm.
Step 4: Calculate focal length (f): \( \frac{1}{f} = \frac{1}{-30} + \frac{1}{-10} \)
\( \frac{1}{f} = \frac{-1 - 3}{30} = \frac{-4}{30} \)
\( f = -7.5 \, cm \)
Step 5: Use the magnification formula: \( m = -\frac{v}{u} \) which gives \( m = -\frac{-10}{-30} = \frac{1}{3} \).
Step 6: Velocity of image (v') is related to velocity of object (u') by the relation: \( v' = -m \cdot u' \).
Step 7: Given object speed = 9 cm/s, hence: \( v' = -\frac{1}{3} \cdot 9 = -3 \, cm/s \).
Therefore, the speed with which the image moves at that instant is 9 cm/s.