Describe:
The locus of points at distances greater than or equal to 35 mm from a given point.
Question types
Loci (Locus and Its Constructions) question types
63 questions across 5 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
63
Questions
5
Question groups
5
Question types
01
[1 Mark Question Answer]
6 Q→02[2 Mark Question Answer]
17 Q→03[3 marks sum]
24 Q→04[5 marks sum]
4 Q→05[4 marks sum]
12 Q→Sample Questions
Loci (Locus and Its Constructions) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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Describe:
The locus of points at distances less than or equal to 2.5 cm from a given point.
Describe:
The locus of points at distances greater than 4 cm from a given point.
Describe:
The locus of points at distances less than 3cm from a given point.
The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth’s surface, who hear the sound exactly one second later.
Describe the locus for questions 1 to 13 given below:
The locus of the centres of all circles passing through two fixed points.
Describe the locus for questions 1 to 13 given below:
The locus of points inside a circle and equidistant from two fixed points on the circumference of the circle.
Describe the locus for questions 1 to 13 given below:
The locus of the door handle, as the door opens .
Describe the locus for questions 1 to 13 given below:
The locus of a stone dropped from the top of a tower.
Describe the locus for questions 1 to 13 given below:
The locus of the moving end of the minute hand of a clock.
Describe the locus for questions 1 to 13 given below:
The locus of a runner, running round a circular track and always keeping a distance of 1.5 m from the inner edge.
Describe the locus for questions 1 to 13 given below:
The locus of points at a distance 2cm from a fixed line.
Plot the points A(2, 9), B(-1, 3) and C (6, 3) on graph paper. On the same graph paper draw the locus of point A so that the area of ΔABC remains the same as A moves.
Construct a triangle ABC, with AB = 6 cm, AC = BC = 9cm. Find a point 4 cm from A and equidistant from B and C.
Construct a triangle ABC, with AB = 5.6 cm, AC = BC = 9.2 cm. Find the points equidistant from AB and AC; and also 2 cm from BC. Measure the distance between the two points obtained.
Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
(i) Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
(ii) Construct the locus of points at a distance of 3.5 cm from A.
(iii.) Construct the locus of points equidistant from AC and BC.
(iv)Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.
Construct a triangle ABC in which angle ABC = 75°, AB= 5cm and BC =6.4cm. Draw perpendicular bisector of side BC and also the bisector of angle ACB. If these bisectors intersect each other at point P; prove that P is equidistant from B and C; and also from AC and BC.
Construct a right angled triangle PQR, in which ∠Q = 90°, hypotenuse PR = 8 cm and QR = 4.5 cm. Draw bisector of angle PQR and let it meets PR at point t. Prove that T is equidistant from PQ and QR.
Construct a triangle ABC, with AB = 7cm, BC = 8cm and ∠ABC = 60°. Locate by construction the point P such that:
(i) P is equidistant from B and C.
(ii) P is equidistant from AB and BC.
Measure and record the length of PB.
(i) P is equidistant from B and C.
(ii) P is equidistant from AB and BC.
Measure and record the length of PB.
Construct a triangle BPC given BC = 5 cm, BP = 4 cm and .
i) complete the rectangle ABCD such that:
a) P is equidistant from AB and BCV
b) P is equidistant from C and D.
ii) Measure and record the length of AB.
Construct an isosceles triangle ABC such that AB = 6cm, BC = AC = 4cm. 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.
Use graph paper for this question. Take 2 cm = 1 unit on both the axis.
(i) Plot the points A(1,1), B(5,3) and C(2,7).
(ii) Construct the locus of points equidistant from A and B.
(iii) Construct the locus of points equidistant from AB and AC.
(iv) locate the point P such that PA = PB and P is equidistant from AB and AC.
(v) Measure and record the length PA in cm.
(i) Plot the points A(1,1), B(5,3) and C(2,7).
(ii) Construct the locus of points equidistant from A and B.
(iii) Construct the locus of points equidistant from AB and AC.
(iv) locate the point P such that PA = PB and P is equidistant from AB and AC.
(v) Measure and record the length PA in cm.
State the locus of a point in a rhombus ABCD, which is equidistant
(i) from AB and AD;
(ii) from the vertices A and C.
(i) from AB and AD;
(ii) from the vertices A and C.
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.
(i) Construct a ΔABC, in which BC = 6cm, AB = 9 cm and angle ABC = 60°.
(ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C.
(iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.
(iv) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(v) Measure and record the length of CQ.
(i) Construct a ΔABC, in which BC = 6cm, AB = 9 cm and angle ABC = 60°.
(ii) Construct the locus of all points inside triangle ABC, which are equidistant from B and C.
(iii) Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.
(iv) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(v) Measure and record the length of CQ.
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