English

A and B Are Fixed Points While Pis a Moving Point, Moving in a Way that It is Always Equidistant from a and B

Advertisements
Advertisements

Question

A and B are fixed points while Pis a moving point, moving in a way that it is always equidistant from A and B. What is the locus of the path traced out by the pcint P? 

Diagram
Advertisements

Solution

The locus of path traced by point P equidistant from A and B is the perpendicular bisector of the line segment joining the two points. 

shaalaa.com
  Is there an error in this question or solution?
Chapter 15: Loci - Exercise 16.1

APPEARS IN

Frank Mathematics Part 2 [English] Class 10 ICSE
Chapter 15 Loci
Exercise 16.1 | Q 12

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Ruler and compasses may be used in this question. All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.

  1. Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and angle ABC = 60°.
  2. Construct the locus of all points inside triangle ABC, which are equidistant from B and C.
  3. Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.
  4. Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
  5. Measure and record the length of CQ.

Construct a triangle BCP given BC = 5 cm, BP = 4 cm and ∠PBC = 45°.

  1. Complete the rectangle ABCD such that:
    1. P is equidistant from AB and BC.
    2. P is equidistant from C and D.
  2. Measure and record the length of AB. 

AB and CD are two intersecting lines. Find a point equidistant from AB and CD, and also at a distance of 1.8 cm from another given line EF. 


Draw and describe the locus in the following case:

The locus of points inside a circle and equidistant from two fixed points on the circle.


Describe completely the locus of a point in the following case:

Midpoint of radii of a circle. 


Describe completely the locus of a point in the following case:

Point in a plane equidistant from a given line. 


Describe completely the locus of a point in the following case:

Centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O. 


Construct a Δ ABC, with AB = 6 cm, AC = BC = 9 cm; find a point 4 cm from A and equidistant from B and C.


Using a ruler and compass only: 
(i) Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, draw a circle with BC as diameter. Find a point 'P' on the circumference of the circle which is equidistant from Ab and BC.
Measure ∠BCP.


Ruler and compass only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.
(ii) Construct the locus of point inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark as P, the point which is equidistant from AB, BC and also equidistant from B and C.
(v) Measure and record the length of PB.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×