Classmate AI
Learn · Solve · Practice
Chapter 12ICSE Class 10 Maths100% Free

Reflection — ICSE Class 10 Maths Important Questions

14 ICSE Class 10 Maths practice questions on Reflection, each with a full model answer, covering 5 topics from the chapter in the question formats used in the exam.

By The Classmate AI Editorial Team

Reviewed by Classmate AI Team · 30 September 2026

14
Questions
5
Topics
4
Key concepts
₹0
With answers

Reflection — ICSE Class 10 Maths Important Questions

Mirror Images on the Coordinate Plane

Your Personal AI Tutor

Teaches Class 8–10 CBSE/ICSE Maths & Science by asking the right questions — not handing over answers.

Start your Freemium plan
Quick answer

Predictable ICSE Reflection questions ask for images under reflection in the xxx-axis (x,y)→(x,−y)(x,y)\to(x,-y)(x,y)(x,-y), the yyy-axis (x,y)→(−x,y)(x,y)\to(-x,y)(x,y)(-x,y) and the origin (x,y)→(−x,−y)(x,y)\to(-x,-y)(x,y)(-x,-y), identifying invariant points, and plotting points with their images on graph paper. Reflection in the lines x=ax=ax=a and y=by=by=b also appears.

Syllabus reference (2026–27): CISCE (Council for the Indian School Certificate Examinations)

About Reflection

In this ICSE Class 10 Maths chapter Reflection you find the image of a point when it is reflected in the coordinate axes, in the origin, and in lines parallel to the axes. You also identify invariant points and plot points and their images on graph paper to name the figure formed.

Reflection in the $x$-axisReflection in the $y$-axisReflection in the originInvariant pointsPlotting images on graph paper

Key concepts & formulas

Reflection in the axes

Mx:(x,y)→(x,−y)M_x:(x,y)\to(x,-y)M_x:(x,y)(x,-y) (reflection in the xxx-axis); My:(x,y)→(−x,y)M_y:(x,y)\to(-x,y)M_y:(x,y)(-x,y) (reflection in the yyy-axis).

Reflection in the origin

(x,y)→(−x,−y)(x,y)\to(-x,-y)(x,y)(-x,-y). Reflecting in the xxx-axis and then the yyy-axis (in either order) gives the same result as reflection in the origin.

Invariant points

A point is invariant if its image is itself. Under MxM_xM_x every point on the xxx-axis is invariant; under MyM_yM_y every point on the yyy-axis is invariant.

Reflection in $x=a$ and $y=b$

(x,y)→(2a−x, y)(x,y)\to(2a-x,\,y)(x,y)(2a-x,\,y) for the line x=ax=ax=a; (x,y)→(x, 2b−y)(x,y)\to(x,\,2b-y)(x,y)(x,\,2b-y) for the line y=by=by=b.

Free download

Get all 14 Reflection questions as a PDF

The full question bank with model answers — perfect for offline revision and last-minute practice.

Free · No spam · Unsubscribe anytime

Important questions with answers

Try each on paper first, then reveal the model answer to check your method.

Multiple-choice questions (1 mark)

Q1MCQEasy1 mark

The image of the point (3,−5)(3,-5)(3,-5) under reflection in the xxx-axis is:

  1. (a)

    (3,5)(3,5)(3,5)

  2. (b)

    (−3,−5)(-3,-5)(-3,-5)

  3. (c)

    (−3,5)(-3,5)(-3,5)

  4. (d)

    (−5,3)(-5,3)(-5,3)

Show model answer

Answer: (a) (3,5)(3,5)(3,5).

Reflection in the xxx-axis sends (x,y)→(x,−y)(x,y)\to(x,-y)(x,y)(x,-y), so (3,−5)→(3,5)(3,-5)\to(3,5)(3,-5)(3,5).

Still stuck? Ask the AI tutor to explain this step by step →
Q2MCQEasy1 mark

The image of the point (4,7)(4,7)(4,7) under reflection in the yyy-axis is:

  1. (a)

    (−4,7)(-4,7)(-4,7)

  2. (b)

    (4,−7)(4,-7)(4,-7)

  3. (c)

    (−4,−7)(-4,-7)(-4,-7)

  4. (d)

    (7,4)(7,4)(7,4)

Show model answer

Answer: (a) (−4,7)(-4,7)(-4,7).

Reflection in the yyy-axis sends (x,y)→(−x,y)(x,y)\to(-x,y)(x,y)(-x,y), so (4,7)→(−4,7)(4,7)\to(-4,7)(4,7)(-4,7).

Still stuck? Ask the AI tutor to explain this step by step →
Q3MCQModerate1 mark

The point (−2,6)(-2,6)(-2,6) is reflected in the origin. Its image is:

  1. (a)

    (2,−6)(2,-6)(2,-6)

  2. (b)

    (−2,−6)(-2,-6)(-2,-6)

  3. (c)

    (2,6)(2,6)(2,6)

  4. (d)

    (6,−2)(6,-2)(6,-2)

Show model answer

Answer: (a) (2,−6)(2,-6)(2,-6).

Reflection in the origin sends (x,y)→(−x,−y)(x,y)\to(-x,-y)(x,y)(-x,-y), so (−2,6)→(2,−6)(-2,6)\to(2,-6)(-2,6)(2,-6).

Still stuck? Ask the AI tutor to explain this step by step →
Q4MCQHOTS1 mark

The image of the point (−3,4)(-3,4)(-3,4) under reflection in the line x=1x=1x=1 is:

  1. (a)

    (5,4)(5,4)(5,4)

  2. (b)

    (−5,4)(-5,4)(-5,4)

  3. (c)

    (5,−4)(5,-4)(5,-4)

  4. (d)

    (−1,4)(-1,4)(-1,4)

Show model answer

Answer: (a) (5,4)(5,4)(5,4).

Reflection in x=ax=ax=a sends (x,y)→(2a−x,y)(x,y)\to(2a-x,y)(x,y)(2a-x,y). With a=1a=1a=1: (2(1)−(−3), 4)=(5,4)(2(1)-(-3),\,4)=(5,4)(2(1)-(-3),\,4)=(5,4).

Still stuck? Ask the AI tutor to explain this step by step →

Want every Reflection question solved live, at your pace?

Practise free with the AI tutor →

Assertion–Reason questions (1 mark)

Q5Assertion–ReasonModerate1 mark

Assertion (A): The point (0,5)(0,5)(0,5) is invariant under reflection in the yyy-axis.

Reason (R): Every point on the yyy-axis maps to itself under reflection in the yyy-axis.

  1. (a)

    Both A and R are true and R is the correct explanation of A

  2. (b)

    Both A and R are true but R is not the correct explanation of A

  3. (c)

    A is true but R is false

  4. (d)

    A is false but R is true

Show model answer

Answer: (a) My(0,5)=(−0,5)=(0,5)M_y(0,5)=(-0,5)=(0,5)M_y(0,5)=(-0,5)=(0,5), so the point is invariant, and since it lies on the yyy-axis, R correctly explains A.

Still stuck? Ask the AI tutor to explain this step by step →

Very short answer questions (2 marks)

Q6Very ShortEasy2 marks

Find the image of the point (6,−2)(6,-2)(6,-2) under reflection in (i) the xxx-axis, (ii) the origin.

Show model answer

(i) Mx:(6,−2)→(6,2).M_x:(6,-2)\to(6,2).M_x:(6,-2)(6,2).

(ii) Origin: (6,−2)→(−6,2).(6,-2)\to(-6,2).(6,-2)(-6,2).

Still stuck? Ask the AI tutor to explain this step by step →
Q7Very ShortModerate2 marks

The image of a point PPP under reflection in the xxx-axis is (−4,5)(-4,5)(-4,5). Find (i) the coordinates of PPP, and (ii) the image of PPP under reflection in the yyy-axis.

Show model answer

(i) Since Mx:(x,y)→(x,−y)M_x:(x,y)\to(x,-y)M_x:(x,y)(x,-y), if the image is (−4,5)(-4,5)(-4,5) then P=(−4,−5).P=(-4,-5).P=(-4,-5).

(ii) My(−4,−5)=(4,−5).M_y(-4,-5)=(4,-5).M_y(-4,-5)=(4,-5).

Still stuck? Ask the AI tutor to explain this step by step →
Q8Very ShortModerate2 marks

(i) Find the image of the point (2,−3)(2,-3)(2,-3) under reflection in the line y=1y=1y=1. (ii) Name the invariant point of this reflection that lies on the yyy-axis.

Show model answer

(i) Reflection in y=by=by=b sends (x,y)→(x, 2b−y)(x,y)\to(x,\,2b-y)(x,y)(x,\,2b-y). With b=1b=1b=1: (2, 2−(−3))=(2,5)(2,\,2-(-3))=(2,5)(2,\,2-(-3))=(2,5).

(Check: (2,−3)(2,-3)(2,-3) and (2,5)(2,5)(2,5) are both 444 units from the line y=1y=1y=1.)

(ii) Only points on the line y=1y=1y=1 are invariant. The one on the yyy-axis is (0,1)(0,1)(0,1).

Still stuck? Ask the AI tutor to explain this step by step →

Short answer questions (3 marks)

Q9Short AnswerModerate3 marks

Under reflection in a line, the point (−2,0)(-2,0)(-2,0) is mapped to (2,0)(2,0)(2,0), and the point (5,−6)(5,-6)(5,-6) is mapped to (−5,−6)(-5,-6)(-5,-6).

(i) Name the line of reflection.

(ii) Find the image of (−4,3)(-4,3)(-4,3) in this line.

(iii) Which points are invariant under this reflection?

Show model answer

(i) In both cases the xxx-coordinate changes sign and the yyy-coordinate stays the same: (x,y)→(−x,y)(x,y)\to(-x,y)(x,y)(-x,y). This is reflection in the yyy-axis (the line x=0x=0x=0).

(ii) (−4,3)→(4,3)(-4,3)\to(4,3)(-4,3)(4,3).

(iii) A point is its own image only if −x=x-x=x-x=x, i.e. x=0x=0x=0. So every point on the yyy-axis is invariant.

Still stuck? Ask the AI tutor to explain this step by step →
Q10Short AnswerEasy3 marks

Plot the point A(1,2)A(1,2)A(1,2) on graph paper. Mark A′A'A', its image under reflection in the xxx-axis, and A′′A''A'', its image under reflection in the yyy-axis. Write the coordinates of A′A'A' and A′′A''A''.

Show model answer

A′=Mx(1,2)=(1,−2)A'=M_x(1,2)=(1,-2)A'=M_x(1,2)=(1,-2) and A′′=My(1,2)=(−1,2).A''=M_y(1,2)=(-1,2).A''=M_y(1,2)=(-1,2).

ICSE Class 10 Maths — Reflection: Plot the point A(1,2) on graph paper. Mark A', its image under reflection in the x-axis, and A'', its image under reflection in the y-axis. Write
Still stuck? Ask the AI tutor to explain this step by step →
Q11Short AnswerHOTS3 marks

For the point (3,5)(3,5)(3,5), show that reflecting in the xxx-axis and then in the yyy-axis gives the same image as a single reflection in the origin.

Show model answer

Reflect in the xxx-axis: Mx(3,5)=(3,−5).M_x(3,5)=(3,-5).M_x(3,5)=(3,-5).

Now reflect this in the yyy-axis: My(3,−5)=(−3,−5).M_y(3,-5)=(-3,-5).M_y(3,-5)=(-3,-5).

Reflection of (3,5)(3,5)(3,5) in the origin: (x,y)→(−x,−y)(x,y)\to(-x,-y)(x,y)(-x,-y) gives (−3,−5).(-3,-5).(-3,-5).

Both routes give (−3,−5)(-3,-5)(-3,-5), so reflection in the xxx-axis followed by the yyy-axis equals reflection in the origin.

Still stuck? Ask the AI tutor to explain this step by step →

Long answer questions (5 marks)

Q12Long AnswerModerate5 marks

The point A(4,3)A(4,3)A(4,3) is given. Let BBB be its image under reflection in the yyy-axis, CCC its image under reflection in the origin, and DDD its image under reflection in the xxx-axis. (i) Write the coordinates of BBB, CCC and DDD. (ii) Name the figure ABCDABCDABCD. (iii) Find its area.

Show model answer

(i) B=My(4,3)=(−4,3)B=M_y(4,3)=(-4,3)B=M_y(4,3)=(-4,3); C=(−4,−3)C=(-4,-3)C=(-4,-3) (origin); D=Mx(4,3)=(4,−3).D=M_x(4,3)=(4,-3).D=M_x(4,3)=(4,-3).

(ii) The four points A(4,3), B(−4,3), C(−4,−3), D(4,−3)A(4,3),\,B(-4,3),\,C(-4,-3),\,D(4,-3)A(4,3),\,B(-4,3),\,C(-4,-3),\,D(4,-3) form a rectangle (its sides are parallel to the axes).

(iii) Length AB=8AB=8AB=8 units and breadth AD=6AD=6AD=6 units, so area =8×6=48=8\times6=48=8×6=48 square units.

ICSE Class 10 Maths — Reflection: The point A(4,3) is given. Let B be its image under reflection in the y-axis, C its image under reflection in the origin, and D its image under re
Still stuck? Ask the AI tutor to explain this step by step →
Q13Long AnswerHOTS5 marks

The triangle with vertices P(1,2)P(1,2)P(1,2), Q(4,2)Q(4,2)Q(4,2) and R(4,5)R(4,5)R(4,5) is reflected in the xxx-axis to give triangle P′Q′R′P'Q'R'P'Q'R'. (i) Write the coordinates of P′P'P', Q′Q'Q', R′R'R'. (ii) Find the area of triangle PQRPQRPQR. (iii) State the relation between the areas of the two triangles.

Show model answer

(i) MxM_xM_x sends (x,y)→(x,−y)(x,y)\to(x,-y)(x,y)(x,-y): P′=(1,−2), Q′=(4,−2), R′=(4,−5).P'=(1,-2),\ Q'=(4,-2),\ R'=(4,-5).P'=(1,-2), Q'=(4,-2), R'=(4,-5).

(ii) △PQR\triangle PQRPQR is right-angled at QQQ with base PQ=3PQ=3PQ=3 and height QR=3QR=3QR=3, so area =12×3×3=4.5=\tfrac12\times3\times3=4.5=12×3×3=4.5 square units.

(iii) Reflection preserves size and shape, so △P′Q′R′\triangle P'Q'R'P'Q'R' is congruent to △PQR\triangle PQRPQR and also has area 4.54.54.5 square units.

ICSE Class 10 Maths — Reflection: The triangle with vertices P(1,2), Q(4,2) and R(4,5) is reflected in the x-axis to give triangle P'Q'R'. (i) Write the coordinates of P', Q', R'.
Still stuck? Ask the AI tutor to explain this step by step →

Case-based questions (4 marks)

Q14Case-basedModerate4 marks

A graphic designer places a key point of a logo at K(3,5)K(3,5)K(3,5) on a coordinate grid and creates images of it by reflection.

(i) Find the image of KKK under reflection in the line y=2y=2y=2.

(ii) Find the image of KKK under reflection in the line x=−1x=-1x=-1.

(iii) Which points of the grid stay fixed when the logo is reflected in the line y=2y=2y=2?

(iv) The designer wants the image of KKK to be (−7,5)(-7,5)(-7,5). In which line x=ax=ax=a must KKK be reflected?

Show model answer

(i) Reflection in y=2y=2y=2: (x,y)→(x, 4−y)(x,y)\to(x,\,4-y)(x,y)(x,\,4-y), so K→(3,−1)K\to(3,-1)K(3,-1).

(ii) Reflection in x=−1x=-1x=-1: (x,y)→(−2−x, y)(x,y)\to(-2-x,\,y)(x,y)(-2-x,\,y), so K→(−5,5)K\to(-5,5)K(-5,5).

(iii) Every point on the line y=2y=2y=2 is invariant, for example (0,2)(0,2)(0,2) and (3,2)(3,2)(3,2).

(iv) Reflection in x=ax=ax=a sends (3,5)→(2a−3, 5)(3,5)\to(2a-3,\,5)(3,5)(2a-3,\,5). So 2a−3=−72a-3=-72a-3=-7, giving a=−2a=-2a=-2: the line x=−2x=-2x=-2. (Check: K(3,5)K(3,5)K(3,5) and (−7,5)(-7,5)(-7,5) are both 555 units from x=−2x=-2x=-2.)

Still stuck? Ask the AI tutor to explain this step by step →

All ICSE Class 10 Maths Chapters

GST (Goods and Services Tax)Banking (Recurring Deposit Accounts)Shares and DividendsLinear Inequations (In One Variable)Quadratic EquationsSolving (Simple) Problems Based on Quadratic EquationsRatio and ProportionRemainder and Factor TheoremsMatricesArithmetic ProgressionGeometric ProgressionReflectionSection and Mid-Point FormulaEquation of a LineSimilarity (With Applications to Maps and Models)Loci (Locus and Its Constructions)CirclesTangents and Intersecting ChordsConstructions (Circles)Cylinder, Cone and Sphere (Surface Area and Volume)Trigonometrical IdentitiesHeights and DistancesGraphical Representation (Histograms and Ogives)Measures of Central Tendency (Mean, Median, Quartiles and Mode)Probability

Frequently asked questions

  • Do these Reflection questions follow the latest ICSE syllabus?
    Yes — they are aligned to the CISCE 2026–27 syllabus for ICSE Class 10 Maths, so nothing here is outside the current course.

Stuck on Reflection? Let the AI tutor help

Free to start · Step-by-step Socratic help · ICSE Class 10 Maths

Practise Reflection free →
💬 Share on WhatsApp
Practise Reflection free with the AI tutor →