11 + Interview Questions in REFLECTION IN GENERAL AWARENESS Page 1 InterviewSolution

1.	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”.
Answer» (i) The reflection in x-axis is given by Mx (x, y) = (x, -y). A’ = reflection of A (-3, 2) in the x- axis = (-3, -2). The reflection in origin is given by MO (x, y) = (-x, -y). A” = reflection of A’ (-3, -2) in the origin = (3, 2) (ii) The reflection in y-axis is given by My (x, y) = (-x, y). The reflection of A (-3, 2) in y-axis is (3, 2). Thus, the required single transformation is the reflection of A in the y-axis to the point A”.

1.

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”.

Answer»

(i) The reflection in x-axis is given by Mx (x, y) = (x, -y).

A’ = reflection of A (-3, 2) in the x- axis = (-3, -2).

The reflection in origin is given by MO (x, y) = (-x, -y).

A” = reflection of A’ (-3, -2) in the origin = (3, 2)

(ii) The reflection in y-axis is given by My (x, y) = (-x, y).

The reflection of A (-3, 2) in y-axis is (3, 2).

Thus, the required single transformation is the reflection of A in the y-axis to the point A”.

Discussion

2.	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”.
Answer» (i) The reflection in origin is given by MO (x, y) = (-x, -y). A’ = reflection of A (4, 6) in the origin = (-4, -6) The reflection in y-axis is given by My (x, y) = (-x, y). A” = reflection of A’ (-4, -6) in the y-axis = (4, -6) (ii) The reflection in x-axis is given by Mx (x, y) = (x, -y). The reflection of A (4, 6) in x-axis is (4, -6). Thus, the required single transformation is the reflection of A in the x-axis to the point A”.

2.

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”.

Answer»

(i) The reflection in origin is given by MO (x, y) = (-x, -y).

A’ = reflection of A (4, 6) in the origin = (-4, -6)

The reflection in y-axis is given by My (x, y) = (-x, y).

A” = reflection of A’ (-4, -6) in the y-axis = (4, -6)

(ii) The reflection in x-axis is given by Mx (x, y) = (x, -y).

The reflection of A (4, 6) in x-axis is (4, -6).

Thus, the required single transformation is the reflection of A in the x-axis to the point A”.

Discussion

3.	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» (i) Reflection in y-axis is given by My (x, y) = (-x, y) ∴ A’ = Reflection of A (2, 6) in y-axis = (-2, 6) Similarly, B’ = (3, 5) and C’ = (-4, 7) Reflection in origin is given by MO (x, y) = (-x, -y) ∴ A” = Reflection of A’ (-2, 6) in origin = (2, -6) Similarly, B” = (-3, -5) and C” = (4, -7) (ii) A single transformation which maps triangle ABC to triangle A”B”C” is reflection in x-axis.

3.

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»

(i) Reflection in y-axis is given by My (x, y) = (-x, y)

∴ A’ = Reflection of A (2, 6) in y-axis = (-2, 6)

Similarly, B’ = (3, 5) and C’ = (-4, 7)

Reflection in origin is given by MO (x, y) = (-x, -y)

∴ A” = Reflection of A’ (-2, 6) in origin = (2, -6)

Similarly, B” = (-3, -5) and C” = (4, -7)

(ii) A single transformation which maps triangle ABC to triangle A”B”C” is reflection in x-axis.

Discussion

4.	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.
Answer» (i) We know reflection of a point (x, y) in y-axis is (-x, y). Hence, the point (-2, 0) when reflected in y-axis is mapped to (2, 0). Thus, the mirror line is the y-axis and its equation is x = 0. (ii) Co-ordinates of the image of (-8, -5) in the mirror line (i.e., y-axis) are (8, -5).

4.

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.

Answer»

(i) We know reflection of a point (x, y) in y-axis is (-x, y).

Hence, the point (-2, 0) when reflected in y-axis is mapped to (2, 0).

Thus, the mirror line is the y-axis and its equation is x = 0.

(ii) Co-ordinates of the image of (-8, -5) in the mirror line (i.e., y-axis) are (8, -5).

Discussion

5.	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).
Answer» (a) We know that reflection in the line x = 0 is the reflection in the y-axis. It is given that: Point (-5, 0) on reflection in a line is mapped as (5, 0). Point (-2, -6) on reflection in the same line is mapped as (2, -6). Hence, the line of reflection is x = 0. (b) It is known that M_y (x, y) = (-x, y) Co-ordinates of the image of (5, -8) in the line x = 0 are (-5, -8).

5.

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).

Answer»

(a) We know that reflection in the line x = 0 is the reflection in the y-axis.

It is given that:

Point (-5, 0) on reflection in a line is mapped as (5, 0).

Point (-2, -6) on reflection in the same line is mapped as (2, -6).

Hence, the line of reflection is x = 0.

(b) It is known that M_y (x, y) = (-x, y) Co-ordinates of the image of (5, -8) in the line x = 0 are (-5, -8).

Discussion

6.	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» Reflection in x-axis is given by Mx (x, y) = (x, -y) P’ = Reflection of P(-2, 3) in x-axis = (-2, -3) Reflection in y-axis is given by My (x, y) = (-x, y) Q’ = Reflection of Q(5, 4) in y-axis = (-5, 4) Thus, the co-ordinates of points P’ and Q’ are (-2, -3) and (-5, 4) respectively.

6.

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»

Reflection in x-axis is given by Mx (x, y) = (x, -y)

P’ = Reflection of P(-2, 3) in x-axis = (-2, -3)

Reflection in y-axis is given by My (x, y) = (-x, y)

Q’ = Reflection of Q(5, 4) in y-axis = (-5, 4)

Thus, the co-ordinates of points P’ and Q’ are (-2, -3) and (-5, 4) respectively.

Discussion

7.	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”.
Answer» (i) We know that every point in a line is invariant under the reflection in the same line. Since points (3, 0) and (-1, 0) lie on the x-axis. So, (3, 0) and (-1, 0) are invariant under reflection in x-axis. Hence, the equation of line L₁ is y = 0. Similarly, (0, -3) and (0, 1) are invariant under reflection in y-axis. Hence, the equation of line L₂ is x = 0. (ii) P’ = Image of P (3, 4) in L₁ = (3, -4) Q’ = Image of Q (-5, -2) in L₁ = (-5, 2) (iii) P” = Image of P (3, 4) in L₂ = (-3, 4) Q” = Image of Q (-5, -2) in L₂ = (5, -2) (iv) Single transformation that maps P’ onto P” is reflection in origin.

7.

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”.

Answer»

(i) We know that every point in a line is invariant under the reflection in the same line.

Since points (3, 0) and (-1, 0) lie on the x-axis.

So, (3, 0) and (-1, 0) are invariant under reflection in x-axis.

Hence, the equation of line L₁ is y = 0.

Similarly, (0, -3) and (0, 1) are invariant under reflection in y-axis.

Hence, the equation of line L₂ is x = 0.

(ii) P’ = Image of P (3, 4) in L₁ = (3, -4) Q’ = Image of Q (-5, -2) in L₁ = (-5, 2)

(iii) P” = Image of P (3, 4) in L₂ = (-3, 4) Q” = Image of Q (-5, -2) in L₂ = (5, -2)

(iv) Single transformation that maps P’ onto P” is reflection in origin.

Discussion

8.	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.
Answer» Reflection in y-axis is given by M_y (x, y) = (-x, y) A’ = Reflection of A(4, -1) in y-axis = (-4, -1) Reflection in x-axis is given by M_x (x, y) = (x, -y) B’ = Reflection of B in x-axis = (-2, 5) Thus, B = (-2, -5)

8.

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.

Answer»

Reflection in y-axis is given by M_y (x, y) = (-x, y)

A’ = Reflection of A(4, -1) in y-axis = (-4, -1)

Reflection in x-axis is given by M_x (x, y) = (x, -y)

B’ = Reflection of B in x-axis = (-2, 5) Thus, B = (-2, -5)

Discussion

9.	Find the image of point (4, -6) under the following operations:(i) Mx . My (ii) My . Mx (iii) MO . Mx (iv) Mx . MO (v) MO . My (vi) My . MO Write down a single transformation equivalent to each operation given above. State whether: (a) MO . Mx = Mx . MO(b) My . MO = MO . My
Answer» (i) M_x . M_y (4, -6) = M_x (-4, -6) = (-4, 6) Single transformation equivalent to M_x . M_y is M_O. (ii) M_y . M_x (4, -6) = M_y (4, 6) = (-4, 6) Single transformation equivalent to My . M_x is M_O. (iii) M_O . M_x (4, -6) = M_O (4, 6) = (-4, -6) Single transformation equivalent to M_O . M_x is M_y. (iv) M_x . M_O (4, -6) = M_x (-4, 6) = (-4, -6) Single transformation equivalent to M_x . M_O is M_y. (v) M_O . M_y (4, -6) = M_O (-4, -6) = (4, 6) Single transformation equivalent to MO . M_y is M_x. (vi) M_y . M_O (4, -6) = M_y (-4, 6) = (4, 6) Single transformation equivalent to M_x . M_O is M_x. From (iii) and (iv), it is clear that M_O . M_x = M_x . M_O. From (v) and (vi), it is clear that M_y . M_O = M_O . M_y.

9.

Find the image of point (4, -6) under the following operations:(i) Mx . My (ii) My . Mx (iii) MO . Mx (iv) Mx . MO (v) MO . My (vi) My . MO Write down a single transformation equivalent to each operation given above. State whether: (a) MO . Mx = Mx . MO(b) My . MO = MO . My

Answer»

(i) M_x . M_y (4, -6) = M_x (-4, -6) = (-4, 6)

Single transformation equivalent to M_x . M_y is M_O.

(ii) M_y . M_x (4, -6) = M_y (4, 6) = (-4, 6)

Single transformation equivalent to My . M_x is M_O.

(iii) M_O . M_x (4, -6) = M_O (4, 6) = (-4, -6)

Single transformation equivalent to M_O . M_x is M_y.

(iv) M_x . M_O (4, -6) = M_x (-4, 6) = (-4, -6)

Single transformation equivalent to M_x . M_O is M_y.

(v) M_O . M_y (4, -6) = M_O (-4, -6) = (4, 6)

Single transformation equivalent to MO . M_y is M_x.

(vi) M_y . M_O (4, -6) = M_y (-4, 6) = (4, 6)

Single transformation equivalent to M_x . M_O is M_x.

From (iii) and (iv), it is clear that M_O . M_x = M_x . M_O.

From (v) and (vi), it is clear that M_y . M_O = M_O . M_y.

Discussion

10.	(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”.
Answer» (i) We know M_x (x, y) = (x, -y) P’ (5, -2) = reflection of P (a, b) in x-axis. Thus, the co-ordinates of P are (5, 2). Hence, a = 5 and b = 2. (ii) P” = image of P (5, 2) reflected in y-axis = (-5, 2) (iii) Single transformation that maps P’ to P” is the reflection in origin.

10.

(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”.

Answer»

(i) We know M_x (x, y) = (x, -y)

P’ (5, -2) = reflection of P (a, b) in x-axis.

Thus, the co-ordinates of P are (5, 2). Hence, a = 5 and b = 2.

(ii) P” = image of P (5, 2) reflected in y-axis = (-5, 2)

(iii) Single transformation that maps P’ to P” is the reflection in origin.

Discussion

11.	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.
Answer» (a) Any point that remains unaltered under a given transformation is called an invariant. It is given that P (0, 5) is invariant when reflected in an axis. Clearly, when P is reflected in the y-axis then it will remain invariant. Thus, the required axis is the y-axis. (b) The co-ordinates of the image of Q (-2, 4) when reflected in y-axis is (2, 4). (c) (0, k) on reflection in the origin is invariant. We know the reflection of origin in origin is invariant. Thus, k = 0. (d) Co-ordinates of image of Q (-2, 4) when reflected in origin = (2, -4) Co-ordinates of image of (2, -4) when reflected in x-axis = (2, 4) Thus, the co-ordinates of the point are (2, 4).

11.

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.

Answer»

(a) Any point that remains unaltered under a given transformation is called an invariant.

It is given that P (0, 5) is invariant when reflected in an axis. Clearly, when P is reflected in the y-axis then it will remain invariant. Thus, the required axis is the y-axis.

(b) The co-ordinates of the image of Q (-2, 4) when reflected in y-axis is (2, 4).

(c) (0, k) on reflection in the origin is invariant. We know the reflection of origin in origin is invariant. Thus, k = 0.

(d) Co-ordinates of image of Q (-2, 4) when reflected in origin = (2, -4)

Co-ordinates of image of (2, -4) when reflected in x-axis = (2, 4) Thus, the co-ordinates of the point are (2, 4).

Discussion

Explore topic-wise InterviewSolutions in .

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”.

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”.

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.

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).

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’.

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.

Find the image of point (4, -6) under the following operations:(i) Mx . My (ii) My . Mx (iii) MO . Mx (iv) Mx . MO (v) MO . My (vi) My . MO Write down a single transformation equivalent to each operation given above. State whether: (a) MO . Mx = Mx . MO(b) My . MO = MO . My

(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”.