Reflection

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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.

Table of Contents

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.
Key points about reflection:
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

Q1. Point P(a, b) is reflected in the y-axis to P′(3, – 2). Write down the values of a and b.

Options

(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.

Q2. A point P (-2 , 3) is reflected in the line x = 2, the coordinates of the point of reflection P’ are:

Options

(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).

Q4. Name the figure formed by a triangle and its reflection, when :

(i) An isosceles right-angled triangle is reflected in its hypotenuse.
(ii) A right-angled triangle is reflected in its hypotenuse.
(iii) An isosceles triangle is reflected in its unequal side.
(iv) A scalene triangle is reflected in its greatest side.

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
$\text{Area of trapezium =} \dfrac{1}{2} \space \space \text{(Sum of parallel sides)} × height \\ = \dfrac{1}{2} (BB”+CC”) ×MN \\ = \dfrac{1}{2} (8+6)×3 \\ = \dfrac{14}{2} ×3 \\$ = 21 sq. units.

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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.

Chapter Wise Important Questions for ICSE Board Class 10 Mathematics
Goods and Service Tax (GST)
Banking
Shares and Dividends
Linear inequations
Quadratic Equations in one variable
Ratio and proportion
Factorization
Matrices
Arithmetic Progression
Geometric Progression
Coordinate Geometry
Reflection
Similarity
Loci
Circles
Constructions
Mensuration
Trigonometry
Statistics
Probability

Class 10 Maths Chapter 12
Reflection
Important Questions

Introduction

What is Reflection?

Class 10 Reflection Important Questions and Answers

Q1. Point P(a, b) is reflected in the y-axis to P′(3, – 2). Write down the values of a and b.

Options

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

Q2. A point P (-2 , 3) is reflected in the line x = 2, the coordinates of the point of reflection P’ are:

Options

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

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´´.

Q4. Name the figure formed by a triangle and its reflection, when :

(i) An isosceles right-angled triangle is reflected in its hypotenuse.
(ii) A right-angled triangle is reflected in its hypotenuse.
(iii) An isosceles triangle is reflected in its unequal side.
(iv) A scalene triangle is reflected in its greatest side.

ICSE Class 10 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1. What is a reflection in geometry?

Q2. What is the mirror line or axis of reflection?

Q3. What happens to a figure during reflection?

Q4. What is the mathematical notation for reflection?

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

Class 10 Maths Chapter 12 Reflection Important Questions

Introduction

What is Reflection?

Class 10 Reflection Important Questions and Answers

Q1. Point P(a, b) is reflected in the y-axis to P′(3, – 2). Write down the values of a and b.

Options

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

Q2. A point P (-2 , 3) is reflected in the line x = 2, the coordinates of the point of reflection P’ are:

Options

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

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´´.

Q4. Name the figure formed by a triangle and its reflection, when :

(i) An isosceles right-angled triangle is reflected in its hypotenuse.(ii) A right-angled triangle is reflected in its hypotenuse.(iii) An isosceles triangle is reflected in its unequal side.(iv) A scalene triangle is reflected in its greatest side.

ICSE Class 10 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1. What is a reflection in geometry?

Q2. What is the mirror line or axis of reflection?

Q3. What happens to a figure during reflection?

Q4. What is the mathematical notation for reflection?

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

Class 10 Maths Chapter 12
Reflection
Important Questions

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

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

(i) A´, B´, C´,
(ii) A´´, B´´, C´´.

(i) An isosceles right-angled triangle is reflected in its hypotenuse.
(ii) A right-angled triangle is reflected in its hypotenuse.
(iii) An isosceles triangle is reflected in its unequal side.
(iv) A scalene triangle is reflected in its greatest side.