(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.
(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.
(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.
Video Tutorials For All Subjects
- Theorems Based on Loci
A straight line AB is 8cm long. Draw and describe the locus of a point which is:
(i) always 4 cm from the line AB.
(ii) equidistant from A and B.
Mark the two points X and Y, which are 4cm from AB and equidistant from A and B. describe the figure AXBY.
Construct a triangle ABC, in which AB = 4.2 cm, BC = 6.3 cm and AC = 5cm. Draw perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C.
Draw an ∠ABC = 60°, having AB = 4.6 cm and BC = 5cm. Find a point P equidistant from AB and BC; and also equidistant from A and B.