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Mathematics

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 :

  1. is parallel to AB

  2. is perpendicular to AB

  3. is perpendicular bisector of AB

  4. passes through the mid-point of AB.

Locus

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Answer

Steps of construction :

  1. Draw a line segment AB.

  2. Draw XY, the perpendicular bisector of AB.

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 : Loci, Concise Mathematics Solutions ICSE Class 10.

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.

Hence, Option 3 is the correct option.

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