# Reflection Concise Maths Solutions Chapter-12 for ICSE Class 10th

## Selina Publishers Solutions Chapter-12 Reflection

**Reflection Concise** Maths **Solutions** Chapter-12 for ICSE Class 10th.** Solutions** of Exercise – 12 (A), Exercise – 12 (B), for** Concise **Selina Maths of ICSE Board Class 10th. **Concise Solutions Reflection **Chapter – 12 for ICSE Maths Class 10 is available here. All

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**Concise**Selina of Chapter-12

**Reflection**has been solved according instruction given by council. This is the

**Solutions**of Chapter-12

**Reflection**for ICSE Class 10th. ICSE Maths text book of

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**Reflection Concise Maths Solutions Chapter-12 for ICSE Class 10th**

The **Solutions** of Concise Mathematics Chapter 12 **Reflection** for ICSE Class 10 have been solved. Experience teachers Solved Chapter-12 **Reflection** to help students of class 10th ICSE board. Therefore the ICSE Class 10th Maths **Solutions** of **Concise** Selina Publishers helpful on various topics which are prescribed in most ICSE Maths textbook

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**Exercise- 12(A) ,**

** **

**How to Solve Concise Maths Selina Publications Chapter-12 Reflection**

Note:- Before viewing **Solutions** of Chapter -12 **Reflection **of **Concise **Selina Maths read the Chapter Carefully then solve all example of your text book**. **The Chapter- 12 **Reflection **is main Chapter in ICSE board** .**

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**Exercise-12(A),Reflection Concise Maths Solutions **

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**Question 1.**

**Complete the following table.**

**Answer 1**

We can complete the blanks as under

(a) Reflection in origin

(b) (4, -2)

(c) (0, 6)

(d) Reflection in origin

(e) Reflection in y-axis.

**Question 2.**

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

**Answer 2**

The image of the point is itself the point P with respect to a line l, Then the point lies in the line l.

**Question 3.**

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

**(i) (3, 2)**

**(ii) (-5, 4)**

**(iii) (0, 0)**

**Answer 3**

The co-ordinates of the given points under reflection in x-axis are as under :

(i) (3, -2)

(ii) (-5, -4)

(iii) (0, 0).

**Question 4.**

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

**(i) (6, -3)**

**(ii) (-1, 0)**

**(iii) (-8, -2)**

**Answer 4**

The co-ordinates of the points under reflection in y-axis are :

(i) (-6, -3)

(ii) (1, 0)

(iii) (8, -2)

**Question 5.**

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

**(i) (-2, -4)**

**(ii) (- 2, 7)**

**(iii) (0, 0)**

**Answer 5**

The co-ordinates of the points under reflection in origin are :

(i) (2, 4)

(ii) (2, -7)

(iii) (0, 0)

**Question 6.**

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

**(i) ( -6, 4)**

**(ii) (0, 5)**

**(iii) (3, -4)**

**Answer 6**

The co-ordinates of the points under reflection in the line x = 0, or y-axis are :

(i) (6, 4)

(ii) (0, 5)

(iii) ( -3, -4)

**Question 7.**

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

**(i) (-3, 0)**

**(ii) (8, -5)**

**(iii) (-1, -3)**

**Answer 7**

The co-ordinates of the points under reflection in the line y = 0 or x-axis are :

(i) (-3, 0)

(ii) (8, 5)

(iii) (-1, 3)

**Question 8.**

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

**(i) Find the co-ordinates of P.**

**(ii) Find the co-ordinates of the image of P under reflection in the y-axis.**

**Answer 8**

(i) The co-ordinates of a point P in the x-axis are (-4, 5).

the co-ordinates of P will be (-4, -5)

(ii) Now the co-ordinates of the image of P under reflection in the y-axis will be (4, -5).

**Question 9.**

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

**(i) Find the co-ordinate of P.**

**(ii) Find the co-ordinates of the image of P under reflection in the x-axis.**

**Answer 9**

The co-ordinates of a point P in the origin are (-2, 7)

The co-ordinates of P will be (2, -7)

(ii) and the co-ordinate of the image of P under the reflection in the x-axis will be (2, 7)

**Question 10.**

**The point P (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.**

**Answer 10**

The co-ordinates of P reflected in the origin will be P ( -a, -b).

Again the co-ordinates of image of P’ under reflection in the y-axis is rule be (a, -b).

But the co-ordinates of P’ are given as (4, 6)

a = 4, -b = 6 ⇒ b = -6

**Question 11.**

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

**Answer 11**

The co-ordinates of P reflected to the x-axis will be (x, -y)

and its coordinate will be reflected in the origin P (-x, y).

But the co-ordinates of P’ are (-8, 5)

-x = -8 => x = 8

y = 5

**Question 12.**

**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’.**

**(a) Write down the co-ordinates of A’**

**(b) Write down a single transformation that maps A onto A’**

**Answer 12**

(a) The co-ordinates of A’, the reflected point in x-axis will be ( -3, -2).

(i) the co-ordinates of A’, the reflected points of A’ in the origin will be (3, 2).

(b) The reflection is in y-axis.

**Question 13.**

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

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

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

**Answer 13**

Co-ordinates of point A are (4, 6). The co-ordinate of A’, the image of A as reflected in the origin will be ( -4, -6).

(i) Again the co-ordinates of A’, the image of A’ as reflected in the y-axis will be (4, -6).

(ii) The reflection is in x-axis.

#### .**Question 14.**

**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”.**

**Answer 14**

In ∆ABC. co-ordinates of vertices.

A are (2. 6), B ( -3. 5) and C (4, 7).

Then the co-ordinates of vertices of ∆A’B’C’ when reflected in the y-axis will be A’ ( -2, 6). B’ (3, 5) and C’ ( -4, 7).

Again the co-ordinates of vertices of ∆A”B”C” when reflected in the origin will be A” (2, -6), B” ( -3, -5) and C”(4, -7).

(ii) The reflection of ∆ABC is in x-axis.

**Question 15.**

**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’.**

**Answer 15**

Co-ordinates of P is ( -2, 3) and co-ordinates of Q (5, 4).

Then the co-ordinates of P’ when reflected in x-axis will be (-2, -3)

and the co-ordinates of Q’ when reflected in y-axis will be (-5, 4)

**Question 16.**

**On a graph paper, plot the triangle ABC whose vertices are at the 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 0 (0, 0).**

**Answer 16**

∆ABC whose vertices are A (3, 1), B (5, 0) and C (7, 4).

Now the image of ∆ABC is ∆A’B’C’ under reflection in the origin O (0, 0).

The co-ordinates of the vertice A’, B’ and C’ will be A’ ( -3, -1), B’ (- 5, 0) and C’ ( -7, -4) as shown on the graph.

**Find the image of point (4, -6) under the following operations :**

**Answer 17**

Since the co-ordinates of a given point are (4, -6), then

**Question 17**

**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 the co-ordinates of A’ and B.**

**Answer 18**

A’ is the reflection of point A (4, -1) in the y-axis and its co-ordinates will be (-4, -1)

Co-ordinates of B’, the image of point B are ( -2, 5) in the x-axis.

Co-ordinates of B will be ( -2, -5)

**Question 18.**

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

**Solution:**

(a) The point (-5, 0) is reflected in a line as (5, 0)

Here, x is mapped as -x

Again point (-2, -6) is mapped in the reflection of the same line as (2, -6)

Here x is mapped as -x

The line of reflection will be y-axis

(b) Now the co-ordinates of the image of the point (5, -8) in the same line will be (-5, -8)

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**Solutions of Exercise -12(B), Reflection Concise Maths Solutions **

** **

**Question 1.**

**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’.**

**Answer 11**

(i) Point P (3, 4) is reflected to P’ in x-axis and then its co-ordinates will be (3, -4) again O’ is the image of O (0, 0) reflected in PP’, then co-ordinates of O’ will be (6, 0)

(ii) Length of PP’ = 4 + 4 = 8 units and OO’ = 3 + 3 = 6 units

(iii) Diagonals of OPO’P’ bisect each other at right angles at M.

OPO’P’ is a rhombus.

(iv) The perimeter of quadrilateral OPO’P’ = 5 x 4 = 20 units

(v) The quadrilateral OPO’P’ is a rhombus as rhombus shown on the graph paper.

**Question 12. ****Reflection Concise Maths Solutions **

**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? (2004)**

**Answer 12**

On the given graph, plot the points A(1, 1), B(5, 1). C(4, 2) and D(2, 2) Join AB, BC, CD and DA.

The quadrilateral is of trapezium in shape.

Now points A, B, C and D are reflected in the origin on to A’, B’, C and D’ respectively.

Co-ordinates of A’ are (-1, -1), of B’ are (-5, -1), of C are (-4, -2) and of D’ are (-2, -2).

A’ B, B’C’, CD’ and D’A’ are joined.

Yes, we see that DA A’D’ are collinear.

**Question 13.**

**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 fa)**

**(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. (2005)**

**Answer 13**

Co-ordinates of the given points P and Q, are (0, 5) and (-2, 4) and have been plotted on the graph.

(a) P is invariant in y-axis

(b) Image of Q(-2, 4) is Q’ in years and its Co-ordinates will be (2, 4)

(c) (0, k) on reflections in we origin is also invariant

Co-ordinates will be (0, 0) k = 0

(d) Let Q” be image of Q reflection in his origin.

Again Q” is reflected in x-axis and its image will be Q’ (2, 4)

**Question 14.**

**a) The point P (2, -4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.**

**(b) The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.**

**(c) Name the figure PQR.**

**(d) Find the area of figure PQR.**

**Answer 14 ****Reflection Concise Maths Solutions **

The graph of the solution set is shown by the thick portion of the number line. The solid circle at -3 indicates that the number – 3 is included among the solutions whereas the open circle at 3 indicates that 3 is not included among the solutions.

(c)

(i) Since the point Q is the reflection of the point P (2, – 4) in the line x = 0, the co-ordinates of Q are (2, 4).

(ii) Since R is the reflection of Q (2, 4) about the line x = 0, the co-ordinates of R are (- 2, 4).

(iii) Figure PQR is the right angled triangle PQR.

(d)

Area of ∆PQR = x QR x PQ = x 4 x 8 = 16 sq. units.

**Question 15.**

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

**(i) Reflect A and B in the origin to get the images A’ and B’.**

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

**(iii) State the geometrical name for the figure ABA’ B’**

**(iv) Find its perimeter.**

**Answer 15**

**Question 16.**

**Use graph paper for this question. (Take 2 cm = 1 unit along both x and y axis.**

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

**(i) Reflect points A and B on the y-axis and name them A’ and B’ respectively. Write down their coordinates. k**

**(ii) Name the figure OABCB’A’.**

**(iii) State the line of symmetry of this figure. (2016)**

**Answer 16**

(ii) The figure OABCB’A’ is similar to arrow headed.

(iii) The y-axis is the line of symmetry of figure OABCB’A’.

#### Question 17

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.

**Solution 17**

(i)Plotting A(0,4), B(2,3), C(1,1) and D(2,0).

(ii) Reflected points B'(-2,3), C'(-1,1) and D'(-2,0).

(iii) The figure is symmetrical about x = 0

**End of Reflection Concise Maths Solutions of Chapter-12**

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Answer 6The image of P ( -2, 3) is P’ which is reflected in the line x = 2. The co-ordinates of P’ will be (6, 3) as shown in the graph.

Question 7.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. [1998]Answer 7(i) A point P (a, b) is reflected in v-axis to P’ (2, -3)

Co-ordinates of P will be (2, 3) a = 2, b = 3.

(ii) P” is the image of P, when reflected in the y- axis

Co-ordinates of P” will be ( -2, 3)

(iii) The image of P is P’” reflected in a line parallel to y-axis i.e. x = 4.

Co-ordinates of P”‘ will be (6, 3)

Question 8.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”.Answer 8Co-ordinates of A are (3, 4) and co-ordinates of B are (0, 2)

(a) Co-ordinates, of A’ of A under reflection in the v-axis are (3, -4)

(b) Co-ordinates of B’ of B under reflection in the line AA’ are (6, 2)

(c) Co-ordinates of A” of A under reflection in y-axis are (-3, 4)

(d) Co-ordinates of B” of B under reflection in the line A A” are (0, 8).

Question 9.(a) Plot the points A(3, 5) and B(-2, -4). Use 1 cm = 1 unit on both the axes.(b) A’ is the image of A when reflected in the v-axis. Write down the co-ordinates of A’ and plot it on the graph paper.(c) 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.(d) Write down the geometrical name of the figure AA’ BB’.(e) Name two invariant points under reflectionin the x-axis. [1999]Answer 9(a) The points A (3, 5) and B(-2, -4) have been plotted on the graph.

(b) A’ is the image of A when reflected in the x-axis

Co-ordinates of A’ will be (3, -5)

(c) B’ is the image of B when reflected in y- axis, followed by reflection in the origin.

Co-ordinates will be (-2, 4)

Images A’ and B’ have also been plotted.

(d) Join AA’, A’B, BB’ and B’A the quadrilateral so joined is an isosceles trapezium.

(e) The points C and D whose co-ordinates ! are (3,0) and (-2, 0) are invariant points under reflection in the x-axis.

Question 10.Reflection Concise Maths SolutionsThe 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 of the perpendicular from P to the x-axis, find the co-ordinates of M.(c) If N is the foot of the perpendicular from P’ to the x-axis, find the co-ordinates of N.(d) Name the figure PM P’ N.(e) Find the area of the figure PM P’ N.Answer 10(a) Points P(5, 3) is reflected to P’ in the origin.

Co-ordinates of P’ will be (-5, -3).

(b) PM ⊥ on x-axis.

Co-ordinates of P’ will be (5, 0)

(c) P’N X on x-axis

Coordinates of N will be (-5, 0).

(d) PM, MP’ P’N and N. P are joined which form a parallelogram PMP’N.

(e) Area of || gm PMP’N = 2 (Area of ∆PMN)

= 2 ( x 10 x 3) Sq. cm

= 30 Sq. cm

Question 11.