Reflection Exe-12A Class-10 Concise Maths Solution Ch-12. In this article you would learn co-ordinate of the point on reflection and invariant point. We Provide Step by Step Solutions / Answer of questions for Selina Concise Maths. Visit official Website CISCE for detail information about ICSE Board Class-10 Mathematics.
Reflection Exe-12A Class-10 Concise Maths Solution Ch-12
| Board | ICSE |
| Publications | Selina |
| Subject | Maths |
| Class | 10th |
| Chapter-12 | Reflection |
| Writer | R.K. Bansal |
| Exe-12A | reflection and invariant point |
| Edition | 2025-2026 |
Reflection and Invariant Point
Reflection Exe-12A Class-10 Concise Maths Solution Ch-12
Que-1: Complete the following table.
Point Transformation Image
(a) (5, –7) ——————– (–5, 7)
(b) (4, 2) Reflection in x-axis ——-
(c) ——- Reflection in y-axis (0, 6)
(d) (6, –6) ——————– (–6, 6)
(e) (4, –8) ——————– (–4, –8)
Ans: 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.
Que-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.
Ans: The image of the point is itself the point P with respect to a line l, Then the point lies in the line l.
Que-3: State the co-ordinates of the following points under reflection in x-axis:
(i) (3, 2)
(ii) (-5, 4)
(iii) (0, 0)
Ans: The co-ordinates of the given points under reflection in x-axis are as under :
(i) (3, -2)
(ii) (-5, -4)
(iii) (0, 0).
Que-4: State the co-ordinates of the following points under reflection in y-axis :
(i) (6, -3)
(ii) (-1, 0)
(iii) (-8, -2)
Ans: The co-ordinates of the points under reflection in y-axis are :
(i) (-6, -3)
(ii) (1, 0)
(iii) (8, -2)
Que-5: State the co-ordinates of the following points under reflection in origin :
(i) (-2, -4)
(ii) (- 2, 7)
(iii) (0, 0)
Ans: The co-ordinates of the points under reflection in origin are :
(i) (2, 4)
(ii) (2, -7)
(iii) (0, 0)
Que-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)
Ans: 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)
Que-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)
Ans: 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)
Que-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.
Ans: The co-ordinates of a point P in the x-axis are (-4, 5).
(i) 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).
Que-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.
Ans: The co-ordinates of a point P in the origin are (-2, 7)
(i) 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)
Que-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.
Ans: 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
Que-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.
Ans: 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
Que-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’
Ans:(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.
Que-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’.
Ans: 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.
Que-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”.
Ans: 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.
Que-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’.
Ans: 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)
Que-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).
Ans: ∆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 vertices A’, B’ and C’ will be A’ ( -3, -1), B’ (- 5, 0) and C’ ( -7, -4) as shown on the graph.
Que-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.
Ans: 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)
Que-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).
Ans: (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)
–: Reflection Exe-12A Class-10 Concise Maths Solution Ch-12 :–
Return to :- Selina Concise Solutions for ICSE Class-10 Maths
Thanks
Please Share with Your Friends
