Mathematics
Describe the locus of a point in a rhombus ABCD which is equidistant from
(i) AB and AD
(ii) A and C
Locus
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Answer
(i) Locus of a point equidistant from AB and AD
The locus of a point equidistant from two intersecting lines AB and AD is the angle bisector of the angle formed by those lines i.e. angle bisector of ∠DAB.
Since, diagonals of rhombus bisect the interior angles.
Hence, locus of a point in rhombus ABCD equidistant from AB and AD is the bisector of ∠DAB, i.e., diagonal AC.
(ii) Locus of a point equidistant from A and C
The locus of a point equidistant from two fixed points A and C is the perpendicular bisector of the line segment joining the two points AC.
Since, diagonals of a rhombus always bisect each other at right angles.
Hence, locus of a point in rhombus ABCD equidistant from A and C is the perpendicular bisector of AC, i.e., diagonal BD.
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