MathematicsChapter 9: Geometry and Polygons
Loci
A locus is the set of all points that obey a rule.
Definition
A locus is the set of all points that obey a rule. In plane geometry the usual Class 9 loci are: a circle (fixed distance from a point), a perpendicular bisector (equal distance from two points), and an angle bisector (equal distance from two lines).
Overview
Three standard loci:
Distance From A Point Or From Two Points
Points at distance r from A form a circle centre A. Points equally far from A and B form the perpendicular bisector of AB. That is why the circumcentre of a triangle sits on perpendicular bisectors of the sides.
Examples Garden fence a fixed radius from a tree · Set of points as far from city A as city B · Compass arc while constructing
Distance From Lines
Points at a fixed distance from a straight line form two parallels, one each side. Points inside an angle, equally far from both arms, lie on the angle bisector. That is the in-centre idea in a triangle.
Examples Path 2 m from a wall · Angle bisector construction · Points equidistant from two roads
Explanation
A construction is a drawing that uses ruler and compass to realise a locus. Naming the locus in words ('perpendicular bisector of AB') is the theory; the arcs are the practice.
In simple words
A sketch of 'a few points that seem to fit' is not a locus. The locus is the complete set the rule allows.
Key points
- set of points
- a rule
- circle
- perpendicular bisector
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Loci
Sticky Notes · Quick Revision
Core Idea
- A locus is the set of all points that obey a rule.
Key Points
- set of points
- a rule
Simple Check
- Explain loci in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- A sketch of 'a few points that seem to fit' is not a locus. The locus is the complete set the rule allows.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- set of points
- a rule
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