Selina Solutions Concise Maths Class 10 Chapter 12 Reflection
Concise Maths Class 10 Chapter 12 Reflection Exercise 12(A) Page No: 165
Question 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) |
Solution:
| Point | Transformation | Image | |
| (a) | (5, -7) | Reflection in origin | (-5, 7) |
| (b) | (4, 2) | Reflection in x-axis | (4, -2) |
| (c) | (0, 6) | Reflection in y-axis | (0, 6) |
| (d) | (6, -6) | Reflection in origin | (-6, 6) |
| (e) | (4, -8) | Reflection in y-axis | (-4, -8) |
Question 2. A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.
Solution:
As, the image of the point P is the same point under the reflection in the line l we can say, point P is an invariant point.
Thus, the position of point P remains unaltered.
Question 3. State the co-ordinates of the following points under reflection in x-axis:
(i) (3, 2)
(ii) (-5, 4)
(iii) (0, 0)
Solution:
(i) (3, 2)
The co-ordinates of the given point under reflection in the x-axis are (3, -2).
(ii) (-5, 4)
The co-ordinates of the given point under reflection in the x-axis are (-5, -4).
(iii) (0, 0)
The co-ordinates of the given point under reflection in the x-axis are (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)
Solution
(i) (6, -3)
The co-ordinates of the given point under reflection in the y-axis are (-6, -3).
(ii) (-1, 0)
The co-ordinates of the given point under reflection in the y-axis are (1, 0).
(iii) (-8, -2)
The co-ordinates of the given point under reflection in the y-axis are (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)
Solution:
(i) (-2, -4)
The co-ordinates of the given point under reflection in origin are (2, 4).
(ii) (-2, 7)
The co-ordinates of the given point under reflection in origin are (2, -7).
(iii) (0, 0)
The co-ordinates of the given point under reflection in origin are (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)
Solution:
(i) (-6, 4)
The co-ordinates of the given point under reflection in the line x = 0 are (6, 4).
(ii) (0, 5)
The co-ordinates of the given point under reflection in the line x = 0 are (0, 5).
(iii) (3, -4)
The co-ordinates of the given point under reflection in the line x = 0 are (-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)
Solution:
(i) (-3, 0)
The co-ordinate of the given point under reflection in the line y = 0 is (-3, 0).
(ii) (8, -5)
The co-ordinate of the given point under reflection in the line y = 0 is (8, 5).
(iii) (-1, -3)
The co-ordinate of the given point under reflection in the line y = 0 is (-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.
Solution:
(i) As, Mx (-4, -5) = (-4, 5)
Hence, the co-ordinates of P are (-4, -5).
(ii) Co-ordinates of the image of P under reflection in the y-axis (4, -5).
Question 9. A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).
(i) Find the co-ordinates of P.
(ii) Find the co-ordinates of the image of P under reflection in the x-axis.
Solution:
(i) As, MO (2, -7) = (-2, 7)
Hence, the co-ordinates of P are (2, -7).
(ii) Co-ordinates of the image of P under reflection in the x-axis (2, 7)
Exercise 12(B) Page No: 165
Question 1. Attempt this question on graph paper.
(a) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
(b) Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.
(c) Write down:
(i) the geometrical name of the figure ABB’A’;
(ii) the measure of angle ABB’;
(iii) the image of A” of A, when A is reflected in the origin.
(iv) the single transformation that maps A’ to A”.
Solution:
(c)
(i) From the graph, it’s clearly seen that ABB’A’ is an isosceles trapezium.
(ii) The measure of angle ABB’ is 45°.
(iii) A” = (-3, -2)
(iv) Single transformation that maps A’ to A” is the reflection in y-axis.
Question 2. 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”.
Solution:
(i) We know that, every point in a line is invariant under the reflection in the same line.
As the points (3, 0) and (-1, 0) lie on the x-axis.
Thus, (3, 0) and (-1, 0) are invariant under reflection in x-axis.
Therefore, the equation of line L1 is y = 0.
Similarly, (0, -3) and (0, 1) are also invariant under reflection in y-axis.
Therefore, the equation of line L2 is x = 0.
(ii) P’ = Image of P (3, 4) in L1 = (3, -4)
And, Q’ = Image of Q (-5, -2) in L1 = (-5, 2)
(iii) P” = Image of P (3, 4) in L2 = (-3, 4)
And, Q” = Image of Q (-5, -2) in L2 = (5, -2)
(iv) Single transformation that maps P’ onto P” is reflection in origin.
Question 3. (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”.
Solution:
(i) As, Mx (x, y) = (x, -y)
P’ (5, -2) = reflection of P (a, b) in x-axis.
Hence, the co-ordinates of P are (5, 2).
Thus, 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.
Question 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.
Solution:
(i) We know that, reflection of a point (x, y) in y-axis is (-x, y).
So, the point (-2, 0) when reflected in y-axis is mapped to (2, 0).
Hence, the mirror line is the y-axis and it’s equation is x = 0.
(ii) The co-ordinates of the image of (-8, -5) in the mirror line (i.e., y-axis) are (8, -5).
Question 5. The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.
Solution:
The line y = 3 is a line parallel to x-axis and at a distance of 3 units from it.
Let’s mark the points P (4, 1) and Q (-2, 4).
Now from P, draw a straight line perpendicular to line CD and produce. Mark a point P’ on this line which is at the same distance above CD as P is below it.
Thus, the co-ordinates of P’ are (4, 5).
Similarly, from Q, draw a line perpendicular to CD and mark point Q’ which is at the same distance below CD as Q is above it.
Hence, the co-ordinates of Q’ are (-2, 2).
Question 6. A point P (-2, 3) is reflected in line x = 2 to point P’. Find the coordinates of P’.
Solution:
The line x = 2 is a line parallel to y-axis and at a distance of 2 units from it.
Let’s mark the point P (-2, 3).
From P, draw a straight line perpendicular to line CD and produce. Mark a point on this line which is at the same distance to the right of CD as P is to the left of it.
Hence, the co-ordinates of P’ are (6, 3).
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.
Solution:
A point P (a, b) is reflected in the x-axis to P’ (2, -3).
We know that, Mx (x, y) = (x, -y)
Hence, the co-ordinates of P are (2, 3).
And thus, a = 2 and b = 3.
P” = Image of P reflected in the y-axis = (-2, 3)
P”’ = Reflection of P in the line (x = 4, a line parallel to y-axis and at a distance of 4 units from it) = (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”.
Solution:
(a) A’ = Image of A under reflection in the x-axis = (3, -4)
(b) B’ = Image of B under reflection in the line AA’ (x = 3) = (6, 2)
(c) A” = Image of A under reflection in the y-axis = (-3, 4)
(d) B” = Image of B under reflection in the line AA” (y = 4) = (0, 6)
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