Frank Solutions for Chapter 8 Reflection Class 10 ICSE Mathematics
Exercise 8
1. State the co-ordinates of the images of the following points under reflection in the x-axis:
(i) (3,-9)
(ii) (-7, 5)
(iii) (0, 6)
(iv) (-4,-8)
Answer
(i) (3,-9)
The co-ordinates of the images of the given points under reflection in the x-axis is (3, 9)
(ii) (-7, 5)
The co-ordinates of the images of the given points under reflection in the x-axis is (-7, 5)
(iii) (0, 6)
The co-ordinates of the images of the given points under reflection in the x-axis is (0, 6)
(iv) (-4,-8)
The co-ordinates of the images of the given points under reflection in the x-axis is (-4, 8)
2. State the co-ordinates of the images of the following points under reflection in the y-axis:
(i) (2, 8)
(ii) (-1,-3)
(iii) (5,-6)
(iv) (-4, 7)
Answer
(i) (2, 8)
The co-ordinates of the images of the given points under reflection in the y-axis is (-2, 8)
(ii) (-1,-3)
The co-ordinates of the images of the given points under reflection in the y-axis is (1, -3)
(iii) (5,-6)
The co-ordinates of the images of the given points under reflection in the y-axis is (-5, -6)
(iv) (-4, 7)
The co-ordinates of the images of the given points under reflection in the y-axis is (4, 7)
3. State the co-ordinates of the images of the following points under reflection in the origin:
(i) (-1,-4)
(ii) (2, 7)
(iii) (0, 2)
(iv) (9,-9)
Answer
(i) (-1,-4)
The co-ordinates of the images of the given points under reflection in the origin is (1, 4)
(ii) (2, 7)
The co-ordinates of the images of the given points under reflection in the origin is (-2, -7)
(iii) (0, 2)
The co-ordinates of the images of the given points under reflection in the origin is (0, -2)
(iv) (9,-9)
The co-ordinates of the images of the given points under reflection in the origin is (-9, 9)
4. P’ is the image of P under reflection in the x-axis. If the co-ordinates of P’ are (2, 10), write the co-ordinates of P.
Answer
From the question it is given that, P’ = (2, 10)
Then, the co-ordinates of P under reflection in the x-axis is (2, -10)
5. S’ is the image of S under reflection in the origin. If the co-ordinates of S are (2,-5), write the co-ordinates of S’.
Answer
From the question it is given that, S = (2, -5)
Then, the co-ordinates of S’ under reflection in the origin is (-2, 5)
6. A point P is reflected in the x-axis to P’. P’ is then reflected in the origin to P”. If the co-ordinates of P’ are (-3, 4). Find the co-ordinates of P and P”. Write the single transformation that map P onto P”.
Answer
From the question it is given that,
P’ = (-3, 4)
Then, the co-ordinates of P under reflection in the x-axis is (-3, -4)
Also the co-ordinates of P” under reflection in the origin is (3, -4)
The single transformation = reflection in the y-axis.
7. A point P is reflected in the x-axis. Co-ordinates of its image are (8, -6). Find the co-ordinates of P. Find the co-ordinates of the image of P under reflection in the y-axis.
Answer
From the question it is given that,
P’ = (8, -6)
Then, the co-ordinates of P under reflection in the x -axis is (8, 6)
The co-ordinates of P” under reflection in the y – axis is (-8, 6)
8. A point R (3, -2) is reflected in the origin as R’. Point Q (-7, 1) is reflected in the x-axis as Q’. Write down the co-ordinates of R’ and Q’. Calculate the distance R’ Q’.
Answer
From the question it is given that
A point R = (3, -2)
Then, a point R is reflected in the origin as R’ = (-3, 2)
Point Q = (-7, 1)
Then, a point Q is reflected in the x – axis as Q’ = (-7, -1)
Now, we have to calculate the distance between R’ Q’ = √[(-7 – (-3))2 + (-1 – 2)2]
= √[(-4)2 + (-3)2]
= √[16 + 9]
= √25
= 5 units
9. The points B and C have the co-ordinates (3, 2) and (0, 3). Find B’, the image of B under the reflection in the x-axis and C’, the image of C under the reflection in the line BB’.
Answer
From the question it is given that,
Point B = (3, 2)
Point C = (0, 3)
Then, the reflection of B in the x – axis is B’ = (3, -2)
And the reflection of C in the line BB’ is C’ = (6, 3)
10. A point P is mapped onto P’ under the reflection in the x-axis. P’ is mapped onto P” under the reflection in the origin. If the co-ordinates of P” are (5,-2), write down the co-ordinates of P. State the single transformation that takes place.
Answer
From the question it is given that,
P” = (5, -2)
Then, co-ordinates of P’ = (-5, 2)
Therefore, the co-ordinates of P = (-5, -2)
Single transformation = reflection in the y-axis
11. Write down the co-ordinates of the image of the point (-2, 4) under reflection in the origin and under reflection in the y-axis. What is the distance between the points of reflection?
Answer
Let us assume that S be the Point,
So, S = (-2, 4)
Then, image under reflection in the origin S’ = (2, -4)
And image under reflection in the y-axis S” = (2, 4)
Now, the distance between point of reflection = √[(4 – (-4))2 + (2 – 2)2]
= √[(8)2 + (0)2]
= √64
= 8 units
12. A triangle ABC lies in the co – ordinate plane. The co – ordinates of its vertices are A (2, 3), B (4, -4) and C (6, -7). This triangle is reflected in the line y = 0 on to ΔA’B’C’. ΔA’B’C’ in then reflected in the origin onto ΔA”B”C”. Write down the co-ordinates of ΔA’B’C’ and ΔA”B”C”.
Answer
From the question it is given that,
The co – ordinates of its vertices are A (2, 3), B (4, -4) and C (6, -7)
Then, co-ordinates of ΔA’B’C’ under reflection in the line y = 0.
So, A’ = (2, -3)
B’ = (4, 4)
C’ = (6, 7)
Now, co-ordinates of ΔA”B”C” under reflection in the origin,
A” = (-2, 3)
B” = (-4, -4)
C” = (-6, -7)
13. A point P (-8, 1) is reflected in the x-axis to the point P’. The point P’ is then reflected in the origin to point P”. Write down the co-ordinates of P”. State the single transformation that maps P into P”.
Answer
From the question it is given that, P = (-8, 1)
The co-ordinates of P’ under reflection in the x –axis = (-8, -1)
Then, the co-ordinates of p” under reflection in the origin = (8, 1)
Single transformation = reflection in the y-axis
14. Perform the following operations and state the single transformation that takes place in each.
(i) Mx.My on P (2, -5)
(ii) My.Mo on A (-7, 3)
(iii) Mo.My on B (4, 6)
(iv) Mx.Mo on P (-1, -3)
Answer
(i) Mx.My on P (2, -5)
Mx.My (2, -5)
Mx (-2, -5)
Therefore, reflection in the origin is (-2, 5)
(ii) My.Mo on A (-7, 3)
My.Mo (-7, 3)
My (7, -3)
Therefore, reflection in the x- axis is (-7, -3)
(iii) Mo.My on B (4, 6)
Mo.My (4, 6)
Mo (-4, 6)
Therefore, reflection in the x – axis (4, -6)
(iv) Mx.Mo on P (-1, -3)
Mx.Mo (-1, -3)
Mx (-1, 3)
Therefore, reflection in the y – axis (-1, -3)
15. Find the co – ordinates of the image of A (-5, 4) after reflection in the line.
(i) y = 0
(i) y = 4
Answer
(i) y = 0
Co – ordinates of the image = (-5, (2 × 0) – 4)
= (-5, (0 – 4))
= (-5, -4)
(ii) y = 4
Co – ordinates of the image = (-5, (2 × 4) – 4)
= (-5, (8 – 4))
= (-5, 4)
16. Find the co-ordinates of the image of S (4, - 1) after reflection in the line
(i) x = 0
(ii) y = 5
Answer
(i) x = 0
Co-ordinates of image = (2 × 0 – 4, 1) = (-4, -1)
(ii) y = 5
Co-ordinates of image = (4, 2 × 5 – (-1) = (4, 11)
17. The point P (1, - 1) , Q (4, -1) and R( 4, 3) are reflected in y-axis. Ig=f the images are denoted by P’, Q’ and R’, then
(i) Find the co-ordinates of P’Q’R, Q’ and R’ .
(ii) What kind of figures is formed by RR’Q’Q ?
(iii) Find the perimeter of the figure P’Q’R
Answer
(i) Find the co-ordinates of P’Q’R’, Q’ and R’
18. Point A (1, - 5) is mapped as A’ on reflection in the line y = 1. The point B (- 5, 1) mapped as B’ on reflection in the line y = 4. Write the co-ordinates of A’ and B’. Calculate AB’.
Answer
A (1, -5), the co-ordinates of A’ (1, 2×1 – (-5)) = (1, 7)
B (- 5, 1), the co-ordinates of B’ = (- 5, 2×4 – (1) = (- 5, 7)
19. Point A (4, - 1) is reflected as A’ in the line x = 1. Point B on reflection in the line y = 3 is mapped as B’ (6, - 1). Write the co-ordinates of A’ and B. Write the co-ordinates of mid-point of the line segment A’B’.
Answer
A (4, -1), the co-ordinates of A’ (2 × 1 – 4, - 1) = (- 2, - 1)
