How many practice questions are available for Locus?

SparkEd Math offers 60+ practice questions for Locus across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Locus content free on SparkEd Math?

Yes! All Locus content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Locus differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Locus problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Locus content aligned with the ICSE syllabus?

Yes, all Locus questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Locus — Class 10 ICSE (2025-26)

About Locus — Class 10 ICSE

Determine loci of points satisfying given geometric conditions and apply to constructions. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 16). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Locus

Introduction to Locus: The Path of a Moving Point
Fundamental Loci: Basic Geometric Shapes
Locus and Geometric Constructions
Advanced Locus and Special Cases
Locus: Summary, Revision, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Locus — solved examples for Class 10 ICSE

Example 1easy

Which of the following statements best defines the 'locus of a point' in geometry?

A)A) It is the path traced by a point moving randomly.
B)B) It is a fixed point or set of points that do not move.
C)C) It is the set of all points that satisfy one or more given geometric conditions.
D)D) It is the shortest distance between two points.

Step-by-step solution

The term 'locus' refers to the collection of all points that fulfill a specific geometric condition or set of conditions.
Each point on the locus satisfies the condition, and no point off the locus satisfies it.

Answer: C) It is the set of all points that satisfy one or more given geometric conditions.

Example 2medium

The locus of a point is the ______ traced by the point satisfying certain given geometrical conditions.

A)path
B)region
C)area
D)volume

Step-by-step solution

A locus is defined as the path traced by a point that moves according to one or more specified geometric conditions.
It represents all possible positions of such a moving point.

Answer: path

Example 3hard

Points A and B are 8 cm apart. A point P moves such that it is equidistant from A and B. Simultaneously, P also moves such that its distance from a fixed point C is 5 cm, where C is 3 cm from the midpoint of AB. If the line AB is perpendicular to the line connecting C to the midpoint of AB, how many possible positions are there for point P?

Step-by-step solution

The locus of points equidistant from A and B is the perpendicular bisector of the segment AB. Let M be the midpoint of AB. The perpendicular bisector passes through M.
The locus of points at a distance of 5 cm from C is a circle with center C and radius 5 cm.
Given that C is 3 cm from M and the line AB is perpendicular to CM, the distance from C to the line (perpendicular bisector of AB) is 3 cm.
Since the radius of the circle is 5 cm and the perpendicular distance from C to the line is 3 cm (which is less than 5 cm), the circle intersects the line at two distinct points. Thus, there are 2 possible positions for P.
$Distance (C, line) = 3 cm < Radius (circle) = 5 cm$

Answer: 2

Practice questions on Locus

Q1.easy
What is the locus of a point P such that it is always equidistant from two fixed points A and B?
1. A)A) A circle with AB as diameter.
2. B)B) The perpendicular bisector of the line segment AB.
3. C)C) A line parallel to AB.
4. D)D) The line segment AB itself.
Show answer
Answer: B) The perpendicular bisector of the line segment AB.
Hint: Consider any point on the perpendicular bisector of a segment. What is its relationship to the segment's endpoints?
Q2.easy
The locus of a point that is equidistant from two intersecting straight lines L1 and L2 is:
1. A)A) The pair of angle bisectors of the angles formed by L1 and L2.
2. B)B) A single line perpendicular to both L1 and L2.
3. C)C) A circle tangent to both L1 and L2.
4. D)D) The point of intersection of L1 and L2.
Show answer
Answer: A) The pair of angle bisectors of the angles formed by L1 and L2.
Hint: Recall the property of an angle bisector: any point on it is equidistant from the two arms of the angle.
Q3.easy
A point P moves in such a way that its distance from a fixed point O is always 7 cm. What is the locus of P?
1. A)A) A straight line passing through O.
2. B)B) A line segment of length 7 cm.
3. C)C) A single point O.
4. D)D) A circle with center O and radius 7 cm.
Show answer
Answer: D) A circle with center O and radius 7 cm.
Hint: Imagine a compass with its pivot at point O and pencil 7 cm away. What shape does it draw?
Q4.medium
What is the locus of a point that is equidistant from two distinct fixed points P and Q?
1. A)A circle with PQ as diameter
2. B)The line segment PQ
3. C)The perpendicular bisector of the line segment PQ
4. D)A line parallel to PQ
Show answer
Answer: The perpendicular bisector of the line segment PQ
Hint: Consider any point on this locus. Its distance to P must be equal to its distance to Q.
Q5.medium
The locus of a point equidistant from two intersecting straight lines L1 and L2 is:
1. A)A single line parallel to L1
2. B)A single line perpendicular to L2
3. C)A circle touching both L1 and L2
4. D)A pair of lines bisecting the angles between L1 and L2
Show answer
Answer: A pair of lines bisecting the angles between L1 and L2
Hint: Think about the property of angle bisectors in relation to the sides of the angle.
Q6.medium
A dog is tied to a pole in the garden with a rope of 5 meters. What is the locus of the points the dog can reach?
1. A)A square of side 5m
2. B)A circle of radius 5m
3. C)A line segment of length 5m
4. D)An ellipse
Show answer
Answer: A circle of radius 5m
Hint: The pole is a fixed point, and the rope length is a constant distance.
Q7.hard
A line segment of fixed length 'L' moves such that its endpoints always lie on the x-axis and y-axis respectively. What is the locus of the midpoint of this line segment?
1. A)A straight line
2. B)A circle
3. C)An ellipse
4. D)A parabola
Show answer
Answer: A circle
Hint: Let the endpoints be (x, 0) and (0, y). Use the distance formula for the segment length and the midpoint formula to relate the coordinates of the midpoint.
Q8.hard
Consider a triangle ABC with a fixed base BC. If the vertex A moves such that the angle BAC remains constant, which of the following statements about the locus of A is TRUE?
1. A)The locus of A is a straight line parallel to BC.
2. B)The locus of A is the perpendicular bisector of BC.
3. C)The locus of A is an arc of a circle passing through B and C.
4. D)The locus of A is a circle with BC as diameter.
Show answer
Answer: The locus of A is an arc of a circle passing through B and C.
Hint: Recall the theorem that states that angles subtended by the same chord in the same segment of a circle are equal.
Q9.hard
A circle with center O and radius 'r' is given. A fixed point P lies inside the circle. What is the locus of the midpoints of all chords of the circle that pass through P?
1. A)A straight line segment
2. B)A circle with P as center
3. C)A circle with OP as diameter
4. D)An arc of the original circle
Show answer
Answer: A circle with OP as diameter
Hint: Consider any chord AB passing through P. Let M be its midpoint. Think about the angle formed by OM and the chord AB.

These are 9 of the 60 questions available for Locus. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.