If the line segment bisector divided his original line segment into two equal pieces, and each piece is 2.9 centimeters long, then the original line segment must be the sum of these two pieces.
So, the length of the original line segment can be calculated as: \[ \text{Original length} = 2 \times 2.9 \text{ cm} = 5.8 \text{ cm} \]
Therefore, the length of Andy's original line segment is 5.8 cm.
The answer is: a. 5.8 cm.