Class 10 Maths - ICSE
Loci (Locus and its Constructions)
The chapter 'Loci (Locus and its Constructions)' in ICSE Class 10 Mathematics explores the path traced by a point that moves under a specific geometrical condition. Students learn fundamental locus theorems, such as the locus of points equidistant from two points, two intersecting lines, and parallel lines. Mastering this chapter is crucial for board exams because it forms the theoretical foundation for accurate scale drawing and geometrical constructions using only a ruler and a compass. Questions from this chapter frequently appear as mandatory, high-scoring construction problems in Section B of the ICSE Mathematics paper.
Start Learning FreeKey Concepts
Definition of Locus
A locus is the set of all points satisfying a given geometrical condition or rule.
Equidistant from Two Points
The locus of a point equidistant from two fixed points is the perpendicular bisector of the line segment joining them.
Equidistant from Two Intersecting Lines
The locus of a point equidistant from two intersecting straight lines consists of the pair of angle bisectors of the angles formed by the lines.
Equidistant from a Given Line
The locus of a point at a constant fixed distance from a given straight line is a pair of parallel lines running on either side of the given line.
Equidistant from Two Parallel Lines
The locus of a point equidistant from two parallel lines is a single parallel line lying exactly midway between them.
Important Formulas
Board Exam Info
In the ICSE Class 10 Mathematics examination, this chapter typically carries about 4 to 10 marks. Questions usually appear as a full construction problem in Section B, where students must construct triangles, circumcircles, incircles, or specific points satisfying multiple locus conditions using a ruler and compass.
Frequently Asked Questions
Can I use a protractor for locus constructions in the ICSE exam?
No, ICSE strict rules require all angles and constructions in this chapter to be done using only a sharp pencil, a ruler, and a pair of compasses. Using a protractor may result in a loss of marks.
How do I know which locus theorem to apply in a word problem?
Read the condition carefully: 'equidistant from two points' means draw a perpendicular bisector, while 'equidistant from two lines' means draw the angle bisector.
What is the difference between a locus and a region?
A locus is strictly the exact path or boundary of points meeting a condition, whereas a region (often involving inequalities) represents an area of points satisfying conditions like being 'less than' or 'greater than' a given distance.
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