Mathematics
Describe the locus of a point in a rhombus ABCD which is equidistant from
(i) AB and AD
(ii) A and C
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.
Related Questions
Describe and construct each of the following loci:
(i) The locus of the tip of a minute hand of a watch.
(ii) The locus of the tip of the pendulum of a clock.
(iii) The locus of a point 5 cm from a fixed point O.
(iv) The locus of a point at a distance of 3 cm from a fixed line AB.
(v) The locus of a point equidistant from the arms OA and OB of ∠AOB.
(vi) The locus of the centres of all circles, each of radius 1 cm and touching externally a fixed circle with centre O and radius 3 cm.
(vii) The locus of the centres of all circles to which both the arms of an angle ∠AOB are tangents.
(viii) The locus of a point 1 cm from the circumference of a fixed circle towards the centre O, whose radius is 3 cm.
(ix) The locus of a point 1 cm from the centre of a circle of radius 2.5 cm.
(x) The locus of a stone dropped from a tower.
(xi) AB is a fixed line. State the locus of a point P such that ∠APB = 90°.
Construct a ΔABC in which BC = 5.3 cm, CA = 4.8 cm and AB = 4 cm. Find by construction a point P which is equidistant from BC and AB and also equidistant from B and C.
Construct ∠AOB = 60°. Mark a point P equidistant from OA and OB such that its distance from another given line CD is 3 cm.
ABC is an equilateral triangle of side 3.2 cm. Find the points on AB and AB produced which are 2 cm from BC.