False

As we know that a perpendicular bisector divides a line segment into two equal parts.

So, if A (2, 7) lies on perpendicular bisector of P (6, 5) and Q (0, - 4),

Then AP = AQ

By distance formula;

AQ =

As we can see AP ≠ AQ

Hence, the point A (2, 7) does not lie on the perpendicular bisector of the line segment PQ.