Class X ICSE Maths Chapter Locus Exercise 14
Welcome to our specialized resource for questions on the topic of "Locus," designed to help you explore and master this fundamental concept in geometry. Our extensive question bank covers a variety of concepts, including the definition of locus, different types of loci, and their geometric representations. You will find questions that challenge you to apply the concept of locus to various scenarios, such as finding the paths traced by points under specific conditions. Whether you're a student preparing for exams or simply looking to enhance your understanding of geometric principles, our collection provides the perfect platform to practice and excel in the topic of "Locus."
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Q1 A point moves such that its distance from a fixed line AB is always the same. What is the relation between AB and the path travelled by P?
Q2 A point P moves so that its perpendicular distance from two given lines AB and CD are equal. State the locus of point P.
Q3 P is a fixed point and a point Q moves such that the distance PQ is constant, what is the locus of the path traced out by point Q?
Q4 (i) AB is a fixed line. State the locus of point P so that ∠APB = 90o.
(ii) A and B are fixed points. State the locus of point P so that ∠APB = 90o.
Q5 Draw and describe the locus in each of the following cases:
(i) The locus of points at a distance 2.5 cm from a fixed line.
(ii) The locus of vertices of all isosceles triangles having a common base.
(iii) The locus of points inside a circle and equidistant from two fixed points on the circle.
(iv) The locus of centres of all circles passing through two fixed points.
(v) The locus of a point in rhombus ABCD, which is equidistant from AB and AD.
(vi) The locus of a point in the rhombus ABCD which is equidistant from points A and C.
Q6 Describe completely the locus of points in each of the following cases:
(i) mid-point of radii of a circle.
(ii) centre of a ball, rolling along a straight line on a level floor.
(iii) point in a plane equidistant from a given line.
(iv) point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).
(v) centre of a circle of varying radius and touching two arms of ∠ADC.
(vi) centre of a circle of varying radius and touching a fixed circle, centre O, at a fixed point A on it.
(vii) centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O.
Q7 Using ruler and compasses construct:
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of points equidistant from A and C.
Q8 Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 600. Locate by construction the point P such that:
(i) P is equidistant from B and C and
(ii) P is equidistant from AB and BC
(iii) Measure and record the length of PB.
Q9 A straight line AB is 8 cm long. Locate by construction the locus of a point which is:
(i) Equidistant from A and B.
(ii) Always 4 cm from line AB.
(iii) Mark two points, X and Y, which are 4 cm from AB and equidistant from A and B.
Name the figure AXBY.
Q10 Use rulers and compasses only for this question.
(i) Construct Δ ABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 600.
(ii) Construct the locus of points 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 the point P, which is equidistant from AB and BC, and also equidistant from B and C.
Measure and record the length of PB.
Q11 Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 1050. Hence:
(i) Construct the locus of points equidistant from BA and BC.
(ii) Construct the locus of points equidistant from B and C.
(iii) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.
Q12 In the diagram, A, B and C are fixed collinear points; D is a fixed point outside the line. Locate:
(i) the point P on AB such that CP = DP.
(ii) the points Q such that CQ = DQ = 3 cm. How many such points are possible?
(iii) the points R on AB such that DR = 4 cm. How many such points are possible?
(iv) the points S such that CS = DS and S is 4 cm away from the line CD. How many such points are possible?
(v) Are the points P, Q, R collinear?
(vi) Are the points P, Q, S collinear?
Q13 Points A, B and C represent the position of three towers such that AB = 60 mm, BC = 73 mm and CA = 52 mm. Taking a scale of 10 m to 1 cm, make an accurate drawing of Δ ABC. Find by drawing the location of a point which is equidistant from A, B and C and its actual distance from any of the towers.
Q14 Draw two intersecting lines to include an angle of 300. Use a ruler and compasses to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such points exist?
Q15 Without using a set square or protractor, construct the quadrilateral ABCD in which ∠BAD = 450, AD = AB = 6 cm, BC = 3.6 cm and CD = 5 cm.
(i) Measure ∠BCD.
(ii) Locate point P on BD, which is equidistant from BC and CD.
Q16 Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ∠ABC. Find the point R on AD such that RB = RC. Measure the length of AR.
Q17 Without using set-squares or protractor construct:
(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
(ii) Draw the locus of a point which moves so that it is always 2.5 cm from B.
(iii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
(iv) Mark the point of intersection of the loci with the letter P and measure PC.
Q18 By using ruler and compasses only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and ∠BAC = 900. Locate the point P such that:
(i) P is equidistant from the sides BC and AC.
(ii) P is equidistant from points B and C.
Q19 Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, ∠B = 600, AD = 5 cm and D is equidistant from AB and BC. Measure CD.
Q20 Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R, which are 5 cm from P and also 5 cm from line AB.
Q21 Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm, respectively.
(i) Construct the locus of points inside the circle that are equidistant from A and C. Prove your construction.
(ii) Construct the locus of points inside the circle that are equidistant from AB and AC
Q22 Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 600. Locate by construction the point P such that:
(i) P is equidistant from B and C and
(ii) P is equidistant from AB and BC
(iii) Measure and record the length of PB.
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