Class 9 Math Chapter 11 Loci and Constructions Notes, MCQs, Solutions & Guess Paper

 

Class 9 Math Chapter 11 Loci and Construction is an important and practical chapter in geometry. It helps students understand how to locate points using specific conditions and how to construct geometric figures accurately.

In this article, you will learn the concept of loci, geometric constructions, solved examples, and practice questions, along with a PDF download link for complete notes.

📌 What is Locus?

A locus is the set of all points that satisfy a given condition.

✅ Example:

All points at a fixed distance from a point form a circle

All points equidistant from two points form a perpendicular bisector

👉 These are common examples of loci used in exams.

📌 Types of Loci

🔹 1. Locus of a Point at a Fixed Distance

Forms a circle

Center = fixed point

Radius = given distance

🔹 2. Locus Equidistant from Two Points

Forms a perpendicular bisector

🔹 3. Locus Equidistant from Two Lines

Forms angle bisectors

📌 Geometrical Constructions

Geometrical constructions involve drawing accurate figures using a compass and ruler without measuring tools.

🔹 Common Constructions

✅ 1. Perpendicular Bisector

Steps:

Draw a line segment

Use compass arcs from both ends

Join intersection points

✅ 2. Angle Bisector

Steps:

Draw an angle

Use compass to create arcs

Join intersection point to vertex

✅ 3. Triangle Construction

Using given sides

Using angles and base

📊 Solved Examples

✅ Example 1:

Construct the perpendicular bisector of a line segment.

👉 Solution:

Draw the line

Create arcs from both ends

Join intersection points

✅ Example 2:

Find the locus of points equidistant from two points.

👉 Solution:

Draw perpendicular bisector

📝 Practice Questions

Define locus with an example

Construct a perpendicular bisector

Draw an angle bisector

What is the locus of points equidistant from two lines?

Construct a triangle using given measurements

You can download the complete notes from the link below:

https://drive.google.com/file/d/10YhNZxU324puZLAIUZrz5oEDudxCpoci/view?usp=drivesdk