The locus of a point equidistant from points P(10, 4) and Q(8, 6) is a perpendicular bisector of PQ passing through
A
(9, 5)
B
(0, 4)
C
(5, 9)
D
(4, 0)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
The locus of points equidistant from two fixed points P and Q is the perpendicular bisector of the line segment PQ.
The midpoint M of PQ is found using the midpoint formula:
M = \(\left(\frac{10 + 8}{2},\ \frac{4 + 6}{2} \right)\) = (9, 5).
Thus, the perpendicular bisector of PQ passes through the point (9, 5).
Source: Myschool Past Questions Archive (Record #78168)