Question

The locus of all the points equidistant from two points is the ________ of the line segment joining the two points.

• A. perpendicular bisector
• B. any line
• C. parallel Lines
• D. None of the above

Answer 1

The correct option is A perpendicular bisector

Consider the given line segment AB. Draw a perpendicular bisector for the line AB. We have AO = BO

Now when we consider △ AXO and △ BXO,

We have AX = BX (Given)

AO = BO (Midpoint of the line segment AB)

XO = XO (Common)

△ AXO ≅ △ BXO (By S.S.S)

In the figure, ∠ AOX + ∠ BOX = 180°

$\therefore$ ∠ AOX = ∠ BOX = 90°

Therefore X lies on the perpendicular bisector of AB.