Question

AB is a line segment. A point P moves in such a way that the triangle APB is always an isosceles triangle with base AB. The locus of point P is the line which ______.

Options

• is parallel to AB.

• is perpendicular to AB.

• is perpendicular bisector of AB.

• passes through the mid-point of AB.

Answer 1

AB is a line segment. A point P moves in such a way that the triangle APB is always an isosceles triangle with base AB. The locus of point P is the line which is perpendicular bisector of AB.

Explanation:

Steps of construction:

1. Draw a line segment AB.
2. Draw XY, the perpendicular bisector of AB.

We know that,

Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the two points.

∴ Any point P on the line XY, will be such that PA = PB.