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Selina solutions for Class 10 Maths chapter 12 - Reflection

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Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10 - Shaalaa.com

Chapter 12: Reflection

Exercise 12(A)Exercise 12(B)

Selina solutions for Class 10 Maths Chapter 12 Exercise Exercise 12(A) [Pages 165 - 166]

Exercise 12(A) | Q 1 | Page 165

Complete the following table.

Point Transformation Image
(5,-7)   (-5,7)
(4,2) Reflection in x-axis  
  Reflection in y-axis (0,6)
(6,-6)   (-6,6)
(4,-8)   (-4,-8)
Exercise 12(A) | Q 2 | Page 165

A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.

Exercise 12(A) | Q 3.1 | Page 165

State the co-ordinates of the following points under reflection in x-axis:

 (3, 2)

Exercise 12(A) | Q 3.2 | Page 165

State the co-ordinates of the following points under reflection in x-axis:

(-5, 4) 

Exercise 12(A) | Q 3.3 | Page 165

State the co-ordinates of the following points under reflection in x-axis:

(0, 0)

Exercise 12(A) | Q 4 | Page 165

State the co-ordinates of the following points under reflection in y-axis:

(i) (6, -3)

(ii) (-1, 0)

(iii) (-8, -2)

Exercise 12(A) | Q 5 | Page 165

State the co-ordinates of the following points under reflection in origin:

(i) (-2, -4)

(ii) (-2, 7)

(iii) (0, 0)

Exercise 12(A) | Q 6 | Page 165

State the co-ordinates of the following points under reflection in the line x = 0:

(i) (-6, 4)

(ii) (0, 5)

(iii) (3, -4)

Exercise 12(A) | Q 7 | Page 165

State the co-ordinates of the following points under reflection in the line y = 0:

(i) (-3, 0)

(ii) (8, -5)

(iii) (-1, -3)

Exercise 12(A) | Q 8.1 | Page 165

A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5). Find the co-ordinates of P.

Exercise 12(A) | Q 8.2 | Page 165

A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5). Find the co-ordinates of the image of P under reflection in the y-axis.

Exercise 12(A) | Q 9.1 | Page 165

A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).Find the co-ordinates of P.

Exercise 12(A) | Q 9.2 | Page 165

A point P is reflected in the origin. Co-ordinates of its image are (-2, 7). Find the co-ordinates of the image of P under reflection in the x-axis.

Exercise 12(A) | Q 10 | Page 165

The point (a, b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has co-ordinates (4, 6); evaluate a and b.

Exercise 12(A) | Q 11 | Page 165

The point P (x, y) is first reflected in the x-axis and reflected in the origin to P’. If P’ has co-ordinates (-8, 5); evaluate x and y.

Exercise 12(A) | Q 12 | Page 165

The point A (-3, 2) is reflected in the x-axis to the point A’. Point A’ is then reflected in the origin to point A”.

(i) Write down the co-ordinates of A”.

(ii) Write down a single transformation that maps A onto A”.

Exercise 12(A) | Q 13 | Page 165

The point A (4, 6) is first reflected in the origin to point A’. Point A’ is then reflected in the y-axis to the point A”.

(i) Write down the co-ordinates of A”.

(ii) Write down a single transformation that maps A onto A”.

Exercise 12(A) | Q 14 | Page 165

The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A’B’C’. Triangle A’B’C’ is then reflected in the origin to triangle A”B”C”.

(i) Write down the co-ordinates of A”, B” and C”.

(ii) Write down a single transformation that maps triangle ABC onto triangle A”B”C”.

Exercise 12(A) | Q 15 | Page 165

P and Q have co-ordinates (-2, 3) and (5, 4) respectively. Reflect P in the x-axis to P’ and Q in the y-axis to Q’. State the co-ordinates of P’ and Q’.

Exercise 12(A) | Q 16 | Page 166

On a graph paper, plot the triangle ABC, whose vertices are at points A (3, 1), B (5, 0) and C (7, 4).

On the same diagram, draw the image of the triangle ABC under reflection in the origin O (0, 0).

Exercise 12(A) | Q 17 | Page 166

Point A (4, -1) is reflected as A’ in the y-axis. Point B on reflection in the x-axis is mapped as B’ (-2, 5). Write down the co-ordinates of A’ and B.

Exercise 12(A) | Q 18 | Page 166

The point (-5, 0) on reflection in a line is mapped as (5, 0) and the point (-2, -6) on reflection in the same line is mapped as (2, -6).

(a) Name the line of reflection.

(b) Write down the co-ordinates of the image of (5, -8) in the line obtained in (a).

Selina solutions for Class 10 Maths Chapter 12 Exercise Exercise 12(B) [Pages 170 - 171]

Exercise 12(B) | Q 1 | Page 170

Attempt this question on graph paper.

(a) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.

(b) Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.

(c) Write down:

(i) the geometrical name of the figure ABB’A’;

(ii) the measure of angle ABB’;

(iii) the image of A” of A, when A is reflected in the origin.

(iv) the single transformation that maps A’ to A”.

Exercise 12(B) | Q 2 | Page 170

Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1;

points (0, -3) and (0, 1) are invariant points on reflection in line L2.

(i) Name or write equations for the lines L1 and L2.

(ii) Write down the images of the points P (3, 4) and Q (-5, -2) on reflection in line L1. Name the images as P’ and Q’ respectively.

(iii) Write down the images of P and Q on reflection in L2. Name the images as P” and Q” respectively. (iv) State or describe a single transformation that maps P’ onto p''

Exercise 12(B) | Q 3 | Page 170

(i) Point P (a, b) is reflected in the x-axis to P’ (5, -2). Write down the values of a and b.

(ii) P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.

(iii) Name a single transformation that maps P’ to P”.

Exercise 12(B) | Q 4 | Page 170

The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).

(i) State the name of the mirror line and write its equation.

(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.

Exercise 12(B) | Q 5 | Page 170

The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

Exercise 12(B) | Q 6 | Page 170

A point P (-2, 3) is reflected in line x = 2 to point P’. Find the coordinates of P’.

Exercise 12(B) | Q 7 | Page 170

A point P (a, b) is reflected in the x-axis to P’ (2, -3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.

Exercise 12(B) | Q 8 | Page 170

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:

(a) A’ of A under reflection in the x-axis.

(b) B’ of B under reflection in the line AA’.

(c) A” of A under reflection in the y-axis.

(d) B” of B under reflection in the line AA”.

Exercise 12(B) | Q 9 | Page 170

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.

(iii) B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA’BB’.

(v) Name the invariant points under reflection in the x-axis.

Exercise 12(B) | Q 10 | Page 170

The point P (5, 3) was reflected in the origin to get the image P’.

(a) Write down the co-ordinates of P’.

(b) If M is the foot if the perpendicular from P to the x-axis, find the co-ordinates of M.

(c) If N is the foot if the perpendicular from P’ to the x-axis, find the co-ordinates of N.

(d) Name the figure PMP’N.

(e) Find the area of the figure PMP’N.

Exercise 12(B) | Q 11 | Page 171

The point P (3, 4) is reflected to P’ in the x-axis; and O’ is the image of O (the origin) when reflected in the line PP’.

Write:

(i) the co-ordinates of P’ and O’.

(ii) the length of the segments PP’ and OO’.

(iii) the perimeter of the quadrilateral POP’O’.

(iv) the geometrical name of the figure POP’O’.

Exercise 12(B) | Q 12 | Page 171

A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A’, B’, C’ and D’ respectively. Locate A’, B’, C’ and D’ on the graph sheet and write their co-ordinates .

Are D, A, A’ and D’ collinear?

Exercise 12(B) | Q 13 | Page 171

P and Q have co-ordinates (0, 5) and (-2, 4).

(a) P is invariant when reflected in an axis. Name the axis.

(b) Find the image of Q on reflection in the axis found in (i).

(c) (0, k) on reflection in the origin is invariant. Write the value of k.

(d) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

Exercise 12(B) | Q 14 | Page 171

The points P (1, 2), Q (3, 4) and R (6, 1) are the vertices of PQR.

(a) Write down the co-ordinates of P’, Q’ and R’, if P’Q’R’ is the image of PQR, when reflected in the origin.

(b) Write down the co-ordinates of P”, Q” and R”, if P”Q”R” is the image of PQR, when reflected in the x-axis.

(c) Mention the special name of the quadrilateral QRR”Q” and find its area.

Exercise 12(B) | Q 15 | Page 171

Using a graph paper, plot the point A (6, 4) and B (0, 4).

(a) Reflect A and B in the origin to get the image A’ and B’.

(b) Write the co-ordinates of A’ and B’.

(c) Sate the geometrical name for the figure ABA’B’.

(d) Find its perimeter.

Exercise 12(B) | Q 16 | Page 171

Use graph paper for this question.

(Take 2 cm = 1 unit along both side x-axis and y-axis.)

Plot the points O(0,0), A(-4, 4), B(-3, 0) and C(0, -3).

  1. Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
  2. Name the figure OABCB'A'.
  3.  iii. State the line of symmetry of this figure. [Now symmetry is not in course] 
Exercise 12(B) | Q 17 | Page 171

Use a graph paper for this question: (Take 2cm = 1 unit on both x and y axes) (i) Plot the following points: A(0,4), B(2,3), C(1,1) and D(2,0).

(ii) Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.

(iii) Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.

Chapter 12: Reflection

Exercise 12(A)Exercise 12(B)

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10 - Shaalaa.com

Selina solutions for Class 10 Mathematics chapter 12 - Reflection

Selina solutions for Class 10 Maths chapter 12 (Reflection) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 12 Reflection are Reflection of a Point in a Line, Reflection of a Point in the Origin., Reflection Examples, Reflection Concept, Invariant Points..

Using Selina Class 10 solutions Reflection exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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