ICSE Class 10

General instructions: Answer all questions. Marks are shown in brackets [ ].

Objective

1. 1.
   The co-ordinates of the point (7, -6) after reflection with $y$-axis are:

   1. A. (-7, 6)
   2. B. (7, -6)
   3. C. (-7, -6)
   4. D. (7, 6)
   [1]
2. 2.
   The co-ordinate of the point $(-4, 5)$ after reflection in the line $y = 0$ are:

   1. A. (4, 5)
   2. B. (4, -5)
   3. C. (-4, -5)
   4. D. none of these
   [1]
3. 3.
   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). What are the co-ordinates of A' and B?

   1. A. A' = (-4, -1), B = (-2, -5)
   2. B. A' = (4, 1), B = (2, -5)
   3. C. A' = (-4, 1), B = (-2, 5)
   4. D. A' = (4, -1), B = (-2, 5)
   [1]
4. 4.
   A point lies on the y-axis at a distance of 5 units from the x-axis. What are the coordinates of this point?

   1. A. (5, 0)
   2. B. (0, 5)
   3. C. (5, 5)
   4. D. (0, -5)
   [1]
5. 5.
   Point A(5, -1) is reflected in the x-axis to obtain A' and in the y-axis to obtain A''. What are the coordinates of A' and A'' and the distance between A' and A''?

   1. A. A' = (5, 1), A'' = (-5, -1), Distance = √104 units
   2. B. A' = (-5, 1), A'' = (5, -1), Distance = √100 units
   3. C. A' = (5, -1), A'' = (-5, 1), Distance = √108 units
   4. D. A' = (5, 1), A'' = (-5, 1), Distance = √104 units
   [1]
6. 6.
   A point P(-2, 3) is reflected in the line x = 2 to point P'. What are the co-ordinates of P'?

   1. A. (2, 3)
   2. B. (6, 3)
   3. C. (-6, 3)
   4. D. (-2, 1)
   [1]
7. 7.
   The co-ordinates of point $Q$ obtained from reflection of $P(5, 1)$ in line $y = 3$ are respectively:

   1. A. (-5, 1)
   2. B. (5, -1)
   3. C. (5, 5)
   4. D. (5, 4)
   [1]
8. 8.
   The point $P(3, -2)$ is reflected in the line $y = -1$, the image has co-ordinates:

   1. A. (-3, -2)
   2. B. (3, -4)
   3. C. (3, 4)
   4. D. (3, 0)
   [1]
9. 9.
   Find the reflection of the point P(-2, 8) in the point M(4, -2). What are the coordinates of the reflected point?

   1. A. (10, -12)
   2. B. (6, -6)
   3. C. (2, -10)
   4. D. (10, 4)
   [1]
10. 10.
    Point obtained after reflection of point $(3, 5)$ in the line $y = 1$ is:

    1. A. (3, -3)
    2. B. (-3, 4)
    3. C. (-3, 5)
    4. D. (3, 5)
    [1]
11. 11.
    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 the y-axis, such that x = 4. Which of the following correctly states the values of a, b, P'', and P'''?

    1. A. a = 2, b = 3; P'' = (-2, 3); P''' = (6, 3)
    2. B. a = 2, b = -3; P'' = (-2, -3); P''' = (6, -3)
    3. C. a = -2, b = 3; P'' = (2, 3); P''' = (-6, 3)
    4. D. a = 2, b = 3; P'' = (2, -3); P''' = (4, 3)
    [1]
12. 12.
    If the reflection of the point $P(3, 9)$ in the line $x = a$ is the point $(7, 9)$ the value of $a$ will be:

    1. A. 2
    2. B. 3
    3. C. 4
    4. D. 5
    [1]
13. 13.
    The points P(4, 1) and Q(-2, 4) are reflected in the line y = 3. What are the co-ordinates of P', the image of P, and Q', the image of Q?

    1. A. P' = (4, 5), Q' = (-2, 2)
    2. B. P' = (4, -1), Q' = (-2, 5)
    3. C. P' = (1, 4), Q' = (4, -2)
    4. D. P' = (4, 2), Q' = (-2, 3)
    [1]
14. 14.
    The point $P(3, 2)$ on reflection in $x$-axis is mapped on $P'$. Then $P'$ reflection in the origin is mapped as $P''$. Which of the following is point $P''$?

    1. A. (-3, 2)
    2. B. (-3, -2)
    3. C. (3, 2)
    4. D. (3, -2)
    [1]
15. 15.
    Use the graph paper for this question. Plot the points A(8, 2) and B(6, 4). These two points are vertices of a figure which is symmetrical about x = 6 and y = 2. Complete the figure on the graph. What is the geometrical name of the figure formed?

    1. A. Rectangle
    2. B. Square
    3. C. Rhombus
    4. D. Kite
    [1]
16. 16.
    A point $P(7, -5)$ is first reflected in $x$-axis to point $Q$ and then $Q$ is reflected in $y$-axis to point $R$. The co-ordinates of point $Q$ and $R$ are respectively:

    1. A. (-7, 5) and (7, -5)
    2. B. (-7, 5) and (7, 5)
    3. C. (7, -5) and (-7, 5)
    4. D. (7, 5) and (-7, 5)
    [1]
17. 17.
    The point P(h, k) is first reflected in the x-axis and then reflected in the origin to obtain the point Q(-2, 5). What are the values of h and k?

    1. A. h = 2 and k = 5
    2. B. h = -2 and k = -5
    3. C. h = 2 and k = -5
    4. D. h = -2 and k = 5
    [1]
18. 18.
    Find the coordinates of the image of the point (-3, 4) after it is reflected first in the x-axis and then in the line x = 2.

    1. A. (7, -4)
    2. B. (1, -4)
    3. C. (-3, 4)
    4. D. (7, 4)
    [1]
19. 19.
    The point $P(a, b)$ is first reflected in the origin to $Q$ and then reflected in the $y$-axis to $R$. If $R$ has co-ordinates $(3, -2)$ then the value of $a$ and $b$ are:

    1. A. 3 and 2
    2. B. -3 and 2
    3. C. 3 and -2
    4. D. -3 and -2
    [1]
20. 20.
    The point $P(a, b)$ is first reflected in the origin to $Q$ and then reflected in the $x$-axis to $R$. If $R$ has co-ordinates $(3, -2)$ then the value of $a$ and $b$ are:

    1. A. 3 and 2
    2. B. -3 and 2
    3. C. 3 and -2
    4. D. -3 and -2
    [1]