Introduction:
Boron trifluoride (BF3) is a molecule with a trigonal planar shape. It consists of a central boron atom bonded to three fluorine atoms. When BF3 reacts with a Lewis base, such as a fluoride ion (F-), it forms a tetrafluoroborate ion (BF4-). This reaction involves the transfer of a fluoride ion from the Lewis base to the boron atom, resulting in the formation of a new covalent bond.

Explanation:
The conversion of boron trifluoride to tetrafluoroborate involves changes in both symmetry and bond lengths. Let's explore each of these aspects in detail:

1. Increase in Symmetry:
Symmetry refers to a property of a molecule that describes how its various parts can be interchanged without changing its overall appearance. In the case of BF3, it has a trigonal planar shape and a C3v point group symmetry. On the other hand, the tetrafluoroborate ion (BF4-) has a tetrahedral shape and a Td point group symmetry. Therefore, the conversion of BF3 to BF4- results in an increase in symmetry.

When a molecule undergoes a process that increases its symmetry, it means that its various parts are becoming more equivalent or similar in terms of their positions and interactions. In this case, the conversion of BF3 to BF4- leads to the formation of four equivalent B-F bonds, resulting in increased symmetry.

2. Bond Elongation:
Bond length refers to the distance between the nuclei of two bonded atoms. It is influenced by factors such as the size of the atoms and the strength of the bond. When BF3 reacts with F-, the boron atom accepts an additional electron pair, resulting in the formation of a new covalent bond between boron and one of the fluorine atoms from the fluoride ion.

The addition of this new bond leads to an increase in the average distance between the boron atom and the fluorine atoms, resulting in bond elongation. The elongation of the B-F bonds in the tetrafluoroborate ion compared to BF3 is a consequence of the new bond formation and the redistribution of electron density in the molecule.

Conclusion:
In conclusion, the conversion of boron trifluoride to tetrafluoroborate accompanies an increase in symmetry and bond elongation. The formation of the tetrafluoroborate ion results in a molecule with higher symmetry due to the formation of four equivalent B-F bonds. Additionally, the addition of a new covalent bond between boron and fluoride leads to an elongation of the B-F bonds compared to BF3.