M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 13 locus

Exercises in Chapter 13 locus Grade 10

Locus Exercise 14

Questions in Locus Exercise 14

Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60⁰. Locate by construction the point P such that:

P is equidistant from AB and BC

Draw and describe the locus in each of the following cases:

The locus of a point in the rhombus ABCD which is equidistant from points A and C.

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 the point Q?

Describe completely the locus of points in each of the following cases:

mid-point of radii of a circle.

Describe completely the locus of points in each of the following cases:

centre of a ball, rolling along a straight line on a level floor.

Describe completely the locus of points in each of the following cases:

point in a plane equidistant from a given line.

Describe completely the locus of points in each of the following cases:

point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).

Describe completely the locus of points in each of the following cases:

centre of a circle of varying radius and touching two arms of ∠ADC.

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?

Describe completely the locus of points in each of the following cases:

centre of a circle of varying radius and touching a fixed circle, centre O, at a fixed point A on it.

A point P moves so that its perpendicular distance from two given lines AB and CD are equal. State the locus of the point P.

AB is a fixed line. State the locus of the point P so that ∠APB = 90⁰.

A, B are fixed points. State the locus of the point P so that ∠APB = 60⁰.

Draw and describe the locus in each of the following cases:

The locus of points at a distance 2.5 cm from a fixed line.

Draw and describe the locus in each of the following cases:

The locus of vertices of all isosceles triangles having a common base.

Describe completely the locus of points in each of the following cases:

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

Using ruler and compasses construct:

a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.

Using ruler and compasses construct:

the locus of points equidistant from A and C.

Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60⁰. Locate by construction the point P such that:

P is equidistant from B and C and

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

Name the figure AXBY.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

Equidistant from A and B.

Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60⁰. Locate by construction the point P such that:

Measure and record the length of PB.

In the diagram, A, B and C are fixed collinear points; D is a fixed point outside the line. Locate:

the points Q such that CQ = DQ = 3 cm. How many such points are possible?

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

Always 4 cm from the line AB.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

Mark two points X and Y, which are 4 cm from AB and equidistant from A and B.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

Use ruler and compasses only for this question.

Construct Δ ABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60⁰.

Use ruler and compasses only for this question.

Construct the locus of points inside the triangle which are equidistant from BA and BC.

Use ruler and compasses only for this question.

Construct the locus of points inside the triangle which are equidistant from B and C.

Use ruler and compasses only for this question.

Mark the point P which is equidistant from AB, BC and also equidistant from B and C.

Measure and record the length of PB.

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105⁰. Hence:

Construct the locus of points equidistant from BA and BC.

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105⁰. Hence:

Construct the locus of points equidistant from B and C.

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105⁰. Hence:

Mark the point which satisfies the above two loci as P. Measure and write the length of PC.

In the diagram, A, B and C are fixed collinear points; D is a fixed point outside the line. Locate:

the point P on AB such that CP = DP.

In the diagram, A, B and C are fixed collinear points; D is a fixed point outside the line. Locate:

the points R on AB such that DR = 4 cm. How many such points are possible?

In the diagram, A, B and C are fixed collinear points; D is a fixed point outside the line. Locate:

the points S such that CS = DS and S is 4 cm away from the line CD. How many such points are possible?

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.

Construct the locus of points, inside the circle, that are equidistant from AB and AC.

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.

Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.

Ruler and compasses 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.

Measure and record the length of CQ.

Ruler and compasses 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.

Construct the locus of the vertices of the triangle with BC as base, which are equal in area to Δ ABC.

Ruler and compasses 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.

Construct the locus of all points, inside Δ ABC, which are equidistant from B and C.

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:

P is equidistant from the points B and C.

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 the line AB.

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.

Without using set-squares or protractor construct:

Mark the point of intersection of the loci with the letter P and measure PC.

Without using set square or protractor, construct the quadrilateral ABCD in which ∠BAD = 45⁰, AD = AB = 6 cm, BC = 3.6 cm and CD = 5 cm.

Locate the point P on BD which is equidistant from BC and CD.

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.

Draw two intersecting lines to include an angle of 30⁰. Use 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?

Without using set square or protractor, construct the quadrilateral ABCD in which ∠BAD = 45⁰, AD = AB = 6 cm, BC = 3.6 cm and CD = 5 cm.

Measure ∠BCD.

Points A, B and C represent 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.