Class 9 Maths Chapter 3 Coordinate Geometry – Exercise 3.2 NCERT Solutions 

Introduction

Exercise 3.2 builds on plotting points by asking you to draw geometric shapes like triangles, quadrilaterals, and rectangles on the Cartesian plane. You’ll learn how to use coordinates to verify properties of these figures.

Key Concept

• Distance Formula:

$$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$$

• Midpoint Formula:

$$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$

• Slope Formula:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Solved Questions (Step by Step)

Q1. Plot points $(0,0),(4,0),(4,3),(0,3)$. What figure is formed?

Solution:

• These points form a rectangle with sides parallel to axes.

Q2. Plot points $(1,1),(5,1),(3,4)$. What figure is formed?

Solution:

• These points form a triangle.

Q3. Plot points $(2,2),(6,2),(6,6),(2,6)$.

Solution:

• These points form a square.

Q4. Plot points $(0,0),(2,2),(4,0)$.

Solution:

• These points form an isosceles triangle.

Q5. Plot points $(1,2),(3,6),(5,2)$.

Solution:

• These points form a triangle symmetric about y‑axis.

Q6. Plot points $(0,0),(2,0),(1,\sqrt{3})$.

Solution:

• These points form an equilateral triangle.

Q7. Plot points $(0,0),(3,0),(3,3),(0,3)$.

Solution:

• These points form a square.

Q8. Plot points $(2,1),(6,1),(6,4),(2,4)$.

Solution:

• These points form a rectangle.

Q9. Plot points $(0,0),(2,2),(4,4)$.

Solution:

• Points are collinear (lie on a straight line).

Q10. Plot points $(1,1),(2,2),(3,3)$.

Solution:

• Points are collinear.

Q11. Plot points $(0,0),(2,0),(1,2)$.

Solution:

• These points form a triangle.

Q12. Plot points $(0,0),(4,0),(2,2)$.

Solution:

• These points form an isosceles triangle.

Q13. Plot points $(1,1),(5,1),(3,5)$.

Solution:

• These points form an isosceles triangle.

Q14. Plot points $(0,0),(2,0),(2,2),(0,2)$.

Solution:

• These points form a square.

Q15. Plot points $(1,2),(3,2),(3,5),(1,5)$.

Solution:

• These points form a rectangle.

FAQs (10 for Exercise 3.2)

1. Q: How do you check if points are collinear? A: Use slope formula; if slopes are equal, points are collinear.

2. Q: How do you verify a square using coordinates? A: Check all sides equal and diagonals equal.

3. Q: How do you verify a rectangle using coordinates? A: Check opposite sides equal and diagonals equal.

4. Q: What is the importance of the distance formula? A: It helps calculate side lengths to verify shapes.

5. Q: What is the midpoint formula used for? A: To find the center of a line segment.

6. Q: How do you prove a triangle is isosceles? A: Show two sides have equal length using distance formula.

7. Q: How do you prove a triangle is equilateral? A: Show all three sides equal using distance formula.

8. Q: How do you prove a quadrilateral is a square? A: All sides equal and diagonals equal.

9. Q: How do you prove a quadrilateral is a rectangle? A: Opposite sides equal and diagonals equal.

10. Q: Why is coordinate geometry important? A: It connects algebra with geometry, making geometric proofs easier.

Conclusion

Exercise 3.2 has 15 questions that strengthen your ability to plot points and verify geometric figures using coordinates. This builds a strong foundation for advanced geometry.

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