Question 1

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

Accepted Answer

**Answer: (a) $(3,5)$.** Reflection in the $x$-axis sends $(x,y)	o(x,-y)$, so $(3,-5)	o(3,5)$.

Question 2

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

Accepted Answer

**Answer: (a) $(-4,7)$.** Reflection in the $y$-axis sends $(x,y)	o(-x,y)$, so $(4,7)	o(-4,7)$.

Question 3

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

Accepted Answer

**Answer: (a) $(2,-6)$.** Reflection in the origin sends $(x,y)	o(-x,-y)$, so $(-2,6)	o(2,-6)$.

Question 4

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

Accepted Answer

**Answer: (a) $(5,4)$.** Reflection in $x=a$ sends $(x,y)	o(2a-x,y)$. With $a=1$: $(2(1)-(-3),\,4)=(5,4)$.

Question 5

**Assertion (A):** The point $(0,5)$ is invariant under reflection in the $y$-axis. **Reason (R):** Every point on the $y$-axis maps to itself under reflection in the $y$-axis.

Accepted Answer

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

Question 6

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

Accepted Answer

(i) $M_x:(6,-2)	o(6,2).$ (ii) Origin: $(6,-2)	o(-6,2).$

Question 7

The image of a point $P$ under reflection in the $x$-axis is $(-4,5)$. Find (i) the coordinates of $P$, and (ii) the image of $P$ under reflection in the $y$-axis.

Accepted Answer

(i) Since $M_x:(x,y)	o(x,-y)$, if the image is $(-4,5)$ then $P=(-4,-5).$ (ii) $M_y(-4,-5)=(4,-5).$

Question 8

The point $A(-4,2)$ is given. Find (i) $B$, the image of $A$ under reflection in the origin, (ii) $C$, the image of $A$ under reflection in the $x$-axis, and (iii) state whether $B$ and $C$ have the same $x$-coordinate.

Accepted Answer

(i) Origin: $B=(4,-2).$ (ii) $M_x$: $C=(-4,-2).$ (iii) $B$ has $x$-coordinate $4$ and $C$ has $x$-coordinate $-4$; they are different (they are negatives of each other).

Question 9

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 the coordinates of $A'$ and $A''$.

Accepted Answer

$A'=M_x(1,2)=(1,-2)$ and $A''=M_y(1,2)=(-1,2).$ ```svg ```

Question 10

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

Accepted Answer

Reflect in the $x$-axis: $M_x(3,5)=(3,-5).$ Now reflect this in the $y$-axis: $M_y(3,-5)=(-3,-5).$ Reflection of $(3,5)$ in the origin: $(x,y)	o(-x,-y)$ gives $(-3,-5).$ Both routes give $(-3,-5)$, so reflection in the $x$-axis followed by the $y$-axis equals reflection in the origin.

Question 11

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 reflection in the $x$-axis. (i) Write the coordinates of $B$, $C$ and $D$. (ii) Name the figure $ABCD$. (iii) Find its area.

Accepted Answer

(i) $B=M_y(4,3)=(-4,3)$; $C=(-4,-3)$ (origin); $D=M_x(4,3)=(4,-3).$ (ii) The four points $A(4,3),\,B(-4,3),\,C(-4,-3),\,D(4,-3)$ form a **rectangle** (its sides are parallel to the axes). (iii) Length $AB=8$ units and breadth $AD=6$ units, so area $=8 imes6=48$ square units. ```svg ```

Question 12

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 $P'$, $Q'$, $R'$. (ii) Find the area of triangle $PQR$. (iii) State the relation between the areas of the two triangles.

Accepted Answer

(i) $M_x$ sends $(x,y) o(x,-y)$: $P'=(1,-2),\ Q'=(4,-2),\ R'=(4,-5).$ (ii) $ riangle PQR$ is right-angled at $Q$ with base $PQ=3$ and height $QR=3$, so area $= frac12 imes3 imes3=4.5$ square units. (iii) Reflection preserves size and shape, so $ riangle P'Q'R'$ is congruent to $ riangle PQR$ and also has area $4.5$ square units. ```svg ```

Question 13

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

(i) Find the image of $K$ under reflection in the $x$ -axis.

(ii) Find the image of $K$ under reflection in the $y$ -axis.

(iii) Find the image of $K$ under reflection in the origin.

(iv) Which single reflection above gives the same point as reflecting $K$ first in the $x$ -axis and then in the $y$ -axis?

Accepted Answer

(i) $M_x(3,5)=(3,-5).$

(ii) $M_y(3,5)=(-3,5).$

(iii) Origin: $(3,5)\to(-3,-5).$

(iv) Reflecting first in the $x$ -axis then the $y$ -axis: $(3,5)\to(3,-5)\to(-3,-5)$ , which is the reflection in the origin from part (iii).

Question 14

Are these Reflection important questions free?

Accepted Answer

Yes. All 13 ICSE Class 10 Maths important questions for Reflection are free, with full model answers and no login required.

Question 15

Do these Reflection questions follow the latest ICSE syllabus?

Accepted Answer

Yes — they are aligned to the CISCE latest syllabus syllabus for ICSE Class 10 Maths, so nothing here is outside the current course.

Question 16

How should I practise the Reflection important questions?

Accepted Answer

Attempt each question on paper first, then reveal the model answer to check your method — not just the final result. Re-do anything you got wrong the same day.

Question 17

What types of questions are covered for Reflection?

Accepted Answer

A full mix — multiple-choice questions, assertion–reason questions, very short answer questions, short answer questions, long answer questions, case-based questions — so every format in the ICSE paper is covered.

Question type	Count	Marks
MCQ	4	1
Assertion–Reason	1	1
Very Short	2	2
Short Answer	3	3
Long Answer	2	5
Case-based	1	4

Reflection — Important Questions

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Multiple-choice questions (1 mark)

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Very short answer questions (2 marks)

Short answer questions (3 marks)

Long answer questions (5 marks)

Case-based questions (4 marks)

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