The length of the transverse axis is 6 and the length of the red line segment is 15. How long is the blue line segment?

In an ellipse, the length of the transverse axis is equal to the distance between the two vertices along the major axis, while the red line segment likely represents the length of the semi-major axis. If the transverse axis is 6, the semi-major axis is 3. The blue line segment, which could represent the semi-minor axis, can be found using the relationship of the ellipse, but without additional information about the ellipse's dimensions or orientation, its length cannot be determined with certainty. More context is needed to provide a specific answer.