Reflection

# Class 10 Maths Chapter 12 Reflection Important Questions

Chapter 12 of ICSE Class 10 Mathematics, titled "Reflection," delves into the fascinating world of geometry and transformations. This chapter introduces students to the concept of reflection, a fundamental geometric operation that involves flipping or mirroring objects across a line known as the "mirror line" or "axis of reflection." Here's an introductory overview of reflection questions class 10 ICSE.

## Introduction

The chapter reflection of class 10 ICSE Mathematics, titled "Reflection," is a captivating exploration of geometry and symmetry. In this chapter, students delve into the intriguing concept of reflection, a fundamental geometric transformation that involves mirroring objects across a line, known as the "mirror line" or "axis of reflection."
Here's an introductory overview of Chapter 12 - "Reflection":
"In ICSE Class 10 Mathematics, Chapter 12, 'Reflection,' invites students into the captivating realm of symmetry and geometric transformations. Reflection, the core theme of this chapter, unveils the beauty of symmetry by showcasing how objects can be mirrored or flipped across a line.

## What is Reflection?

Reflection, as we study in the chapter reflection of class 10 ICSE in the context of geometry and mathematics, is a fundamental transformation that involves flipping or mirroring an object or figure across a specific line called the "mirror line" or "axis of reflection." The result of this transformation is a new figure that is a precise copy of the original but is oriented in the opposite direction.
Mirror Line: The mirror line is the central axis or line across which the reflection occurs. It serves as the axis of symmetry, dividing the figure into two equal and mirror-image halves.

Symmetry: Reflection is a transformation that preserves symmetry. The original figure and its reflection are symmetric with respect to the mirror line. This means that corresponding points on both sides of the mirror line are equidistant from it.

Orientation Change: During reflection, the orientation of the figure changes. For example, if you have a letter 'E' and you reflect it horizontally, you get a backward 'E.'

### Class 10 Reflection Important Questions and Answers

#### (a) a = – 5, b = 2(b) a = – 3, b = – 2(c) a = 5, b = – 2(d) a = 2, b = 5

Ans. (b) a = – 3, b = – 2

Explanation:
Co-ordinates of P′(3, –2).
∴ a = 3, b = –2.

#### (a) (2, 3)(b) (4, 3)(c) (6, 3)(d) (8, 3)

Ans. (c) (6, 3)

Explanation:
Globalisation has created conditions for increased job opportunities.

#### Q3. The triangle A(1, 2), B(4, 4) and C(3, 7) is first reflected in the line y = 0 onto triangle A´B´C´ and then triangle A´B´C´ is reflected in the origin onto triangle A´´B´´C´´. Write down the coordinates of :(i) A´, B´, C´,(ii) A´´, B´´, C´´.

Explanation:
(i)     A´ → (1, – 2),
B´ → (4, – 4),
C´ → (3, – 7).

(ii)    A´´ → (– 1, 2),
B´´ → (– 4, 4),
C´´ → (– 3, 7).

Explanation:

#### Q5. The triangle A (1, 2), B (4, 4) and C (3, 7) is first reflected in line y = 0 onto triangle A′B′C′ and then triangle A′B′C′ is reflected in the origin onto triangle A′′B′′C′′.Write down the coordinates of (i) A′, B′, C′, (ii) A′′, B′′, C′′, (iii) Assign the special name to the quadrilateral BCC′′B′′ and find its area.

Explanation:
Given, vertices of triangles are A(1,2), B (4,4), C (3,7).
(a) Coordinates A(1,2), B (4,4), C (3,7).
(b) Coordinates A”=(- 1,2), B”= (-4,4), C”= (3,7).
(c) BCC”B” is a trapezium
Area of trapezium = $$\dfrac{1}{2}$$ (Sum of parallel sides) × height
= $$\dfrac{1}{2}$$ (BB”+CC”) ×MN
= $$\dfrac{1}{2}$$ (8+6)×3
= $$\dfrac{14}{2}$$ ×3
= 21 sq. units.

#### ICSE Class 10 Maths Chapter wise Important Questions

Chapter No. Chapter Name
Chapter 1 Goods and Service Tax (GST)
Chapter 2 Banking
Chapter 3 Shares and Dividends
Chapter 4 Linear inequations
Chapter 5 Quadratic Equations in one variable
Chapter 6 Ratio and proportion
Chapter 7 Factorization
Chapter 8 Matrices
Chapter 9 Arithmetic Progression
Chapter 10 Geometric Progression
Chapter 11 Coordinate Geometry
Chapter 12 Reflection
Chapter 13 Similarity
Chapter 14 Loci
Chapter 15 Circles
Chapter 16 Constructions
Chapter 17 Mensuration
Chapter 18 Trigonometry
Chapter 19 Statistics
Chapter 20 Probability

#### Conclusion

In conclusion, the study of reflection of class 10 ICSE offers students a fascinating exploration of symmetry and geometric transformations. This chapter delves into the fundamental concept of reflecting objects and figures across a mirror line, unveiling the beauty of symmetry and its practical applications in various fields.
Throughout this chapter, students have learned to identify mirror lines, understand the principles governing reflection, and apply these concepts to geometric shapes. Reflection not only enhances students' appreciation of symmetry but also sharpens their problem-solving skills. If you're looking to enhance your skills through additional practice and gain a deeper understanding of the topics covered in the chapter, oswal.io offers an extensive collection of reflection questions class 10 ICSE  to support your quest for a more profound comprehension of the concepts.

#### Q1 : What is a reflection in geometry?

Ans: Reflection is a geometric transformation that involves mirroring an object or figure across a line, called the mirror line, resulting in a symmetrical image.

#### Q2: What is the mirror line or axis of reflection?

Ans: The mirror line is the central line across which the reflection occurs, serving as the axis of symmetry.

#### Q3 : What happens to a figure during reflection?

Ans: During reflection, the orientation of the figure changes. It becomes a mirror image of the original across the mirror line.

#### Q4 : What is the mathematical notation for reflection?

Ans: Reflection is denoted by "R" followed by the mirror line. For example, "R(x-axis)" represents reflection across the x-axis.

#### Q5 : How do you identify whether a figure has reflection symmetry?

Ans: A figure has reflection symmetry if it can be divided into two identical halves when reflected across a mirror line.

## Chapter Wise  Important Questions for ICSE Board Class 10 Mathematics

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