Question

$A$ and $B$ are two fixed points in a plane. If $P$ is a moving point in the plane such that $PA=PB$, then

• A. The locus of $P$ is the line $AB$ itself
• B. The locus of $P$ is a line parallel to $AB$
• C. The point $P$ always makes equilateral triangles with $A,B$
• D. The triangles $PAB$ is isosceles for all positions of $P$

Answer 1

Answer: (D)

The triangles $PAB$ is isosceles for all positions of $P$

Regardless the position of P,

Since PA=PB

Triangle is isosceles.