SYMMETRY, REFLECTION AND ROTATION EDULABZ. (i) (ii) (iii) (iv) INTERNATIONAL. (i) (one) (ii) (none) (iii) (one) (iv) (one)

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1 6 SMMETR, REFLECTION AND ROTATION. Draw the line or lines of symmetry. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (i) (one) (ii) (none) (iii) (one) (iv) (one) (v) (one) (vi) (none) (vii) (four) (viii) (three) (ix) (four). If possible, draw the largest number of lines of symmetry in each case : Math Class VIII Question ank

2 (i) (i) (ii) (iii) (iv) (v) (ii) (v) none (iii) (iv). Examine each of the following figures, carefully, and then draw line of symmetry if possible : (i) (ii) (iii) (iv) Math Class VIII Question ank

3 (i) The figure has no line of symmetry. (ii) The figure has one line of symmetry. (iii) (iv) The figure has lines of symmetry. The figure has one line of symmetry. (v) The figure has two lines of symmetry. Math Class VIII Question ank

4 . Draw all lines of symmetry for each of the following letters. C E F K (i) (ii) (iii) (iv) V M (v) (vi) (vii) (viii) (i) (ii) One line of symmetry. One line of symmetry. (iii) (iv) No line of symmetry. No line of symmetry. (v) Two lines of symmetry (vi) one line of symmetry. (vii) (viii) One line of symmetry. One line of symmetry.. Mark two points P and Q which are. cm apart. Construct the perpendicular bisector of line segment PQ. Math Class VIII Question ank

5 Are the points P and Q symmetric with respect to the perpendicular bisector drawn? P. cm O Q P and Q are symmetric with respect to perpendicular bisector xy. 6. Find the co-ordinates of the following points under reflection in x- axis : (i) (, 8) (ii) (, 0) (iii) (, 0) (iv) (, ) Required point are : (i) (, 8) (ii) (, 0) (iii) (, 0) (iv) (, ) 7. Find the reflection of the following points in y-axis : (i) (9, 0) (ii) (9, 0) (iii) (0, 9) (iv) ( 9, 0) (v) (9, 0) (vi) ( 9, 0) (i) ( 9, 0) (ii) ( 9, 0) (iii) (0, 9) (iv) (9, 0) (v) ( 9, 0) (vi) (9, 0) 8. Construct an angle PQR = 80. Draw its line of symmetry if PQ = QR = 6. cm. Steps of Constructions : (i) First we draw a line segment PQ = 6. cm (ii) With Q as a centre draw a ray making an angle of 80 and cut off QR = 6. cm and join PR. (iii) Draw the angle bisector of PQR. This is the required line of symmetry. Math Class VIII Question ank 6. cm R 80 Q 6. cm l P

6 9. State and explain the types of symmetry possessed by each of the following figures. A A C C E D O A J I G F D H (i) (ii) (iii) A O F Math Class VIII 6 Question ank C A C A (iv) (v) (vi) (i) (a) From figure it is not a linear symmetry because it has no line of symmetry. (b) From figure its a point symmetry because it has point O which is the centre of symmetry. (c) From figure it is a rotational symmetry because it has rotational symmetry of order above the point O. (ii) (a) From figure it is a linear symmetry because it has two lines of symmetry. i.e., The line joining C and H and the line joining the mid points of AJ and EF. (b) From figure it is a point symmetry because it has point O which is the point of symmetry. (c) From figure it is a point symmetry because it has rotational symmetry of order about the point O. (iii) (a) From figure it is not a linear symmetry because it has no line of symmetry. (b) From figure it is a point symmetry because point O is the point of symmetry. O D E O O C D C

7 (c) From figure it is a rotational symmetry because it has rotational symmetry of order about the point O. (iv) (a) From figure it is a linear symmetry because three lines of symmetry which are the lines joining AD, E and CF. (b) From figure it is not a point symmetry because it has no point symmetry. (c) From figure it is a rotational symmetry because it has a rotational symmetry of order three about the point O. (v) (a) From figure it is not a linear symmetry because it has no line of symmetry. (b) From figure it is not a point symmetry because it has no point of symmetry. (c) From figure it is a rotational symmetry because it has a rotational symmetry of order about the point O. (vi) (a) From figure it is not a linear symmetry because it has no line of symmetry. (b) From figure it is a point symmetry because at O, the point symmetry. (c) From figure it is a rotational symmetry it has a rotational symmetry order about the point O. 0. The point P (a, b) is reflected is x-axis and the point P so obtained is reflected in y-axis to get the point M P. If the co-ordinate of P are (, P ), find the values of a and b. The point P (a, b) when reflected in x-axis, will be P (a, b) and when point P (a, b) is reflected in y-axis, will be P ( a, b) 0 Q O 0 R MS is the only line of symmetry of.6 cm PQR. S. Construct a triangle Z in which = Z = Z =. cm. Draw all its lines of symmetry. Math Class VIII 7 Question ank

8 PQ, RS and A are three lines of symmetry passing through midpoints of sides of triangle. P A S. cm 60 Z. Construct a triangle PQR in which PQ = QR =. cm and PQR = 90. Draw all its lines of P symmetry. O is mid point of PR. The figure is isosceles right triangle. O It has only one line of symmetry passing through mid-point of PR.. Mark two points A and 6. cm apart. Construct the line of symmetry so that the points A and are symmetric with respect to this line. Draw perpendicular bisector of A, bisecting A at O. Thus, is the line of symmetry. A Q R 6. cm O R Math Class VIII 8 Question ank

9 . Construct a triangle AC such that A =. cm, C =. cm and = 60. Rotate the triangle AC through (anti-clockwise) about the point A. Are the two triangles congruent? A. cm 60. cm es, AC and A C are congruent.. Plot the points P (, ) and Q (, 7) on the graph paper. Reflect the line segment PQ in the y-axis to P Q. Write down the coordinates of P and Q. Are PQ and P Q equal? Q 7 Q(, 7) (, 7) C P P E(, ) (, ) 6 7 C es, both PQ and P Q are equal. 6. The triangle AC whose vertices are A (, ), (, ) and C (0, ) is reflected in the y-axis to the triangle A C. Write down the Math Class VIII 9 Question ank

10 coordinates of the vertices of triangle A C. Are the two triangles congruent? A (, ), (, ) and C (0, ) The vertices of triangle are reflected in y-axis. A (, ) (, ) C (0, ) (, ) 0 A A (, ) (, ) C (0, ) (, ) AC and A C both are congruent. 7. A point P (, 6) is rotated about the origin through 80 to the point P, write down the coordinates of P graphically (, 6) P 6 P (, 6) Math Class VIII 0 Question ank

11 8. Plot the points P (, ) and Q (, 7) on the graph paper. Rotate the line segment PQ through 80 about the origin to the position P Q. Write down the coordinates of P and Q. Are PQ and P Q equal? Q (, 7) P (, ) P (, ) Q (, 7) oth PQ and P Q are equal. 9. Plot the points A (, ) and (, ) on the graph paper. Rotate the line segment A through 90 clockwise about the origin to the position A. Write down the coordinates of A and. Are A and A equal? (, ) 0 (, ) A (, ) A(, ) Also, A = A. Math Class VIII Question ank

12 0. Plot the points A (, ), (, ) and C (0, ) on the graph paper. Reflect the triangle AC in the x-axis to the triangle A C. Write down the coordinates of the vertices of A C. Are the two triangles congruent? Co-ordinates of A C are A (, ) (, ) C (0,) 6 C (0, ) A (, ) (, ) C(0, ) (, ) 6 A(, ) es AC & A C are congruent.. Plot the points A (, ) and (, ) on the graph paper. Rotate the triangle OA through 80 about O (origin). Find the coordinates of the vertices of this new triangle. A (, ) (, ) 6 (, ) A (, ) So co-ordinate of vertices of new triangle OA are (0, 0) (, ) (, ) Math Class VIII Question ank

13 . Plot the points P (, ) and Q (, 7) on the graph paper. Rotate the line segment PQ through 90 anti-clockwise about the origin to the position P Q. Write down the coordinates of P and Q. P (, ) (, ) P 6 7 Q (7, ) Q (, 7) Co-ordinates of P and Q are (, ) and (7, ). Plot the points A (, 0), (, ), C (, ) D (, ) and E(, ) on the graph paper. Rotate the pentagon ACDE through 90 anticlockwise about the origin to take the position A C D E. Write down the coordinates of the vertices of the pentagon in new position. Coordinates of A (0, ), (,), C (, ), D (, ), E (,). (, ) 0 (, ) D C(, ) (, ) C A (0, ) (, ) E (, ) A (, 0) D (, ) E (, ) Math Class VIII Question ank

14 . The point Q (a, b) is reflected is y-axis and the point Q so obtained is reflected in x-axis to get the point Q. If the coordinates of Q are (, ), find the values of a and b. The point Q (a, b) when reflected in y-axis will be Q ( a, b) and point Q ( a, b) when reflected in x-axis will be Q ( a, b). ut co-ordinates of Q are (, ) a = a = and b = b =. Draw the image figure of the line segment A reflected in x-axis, the co-ordinates of A and being A (, ) and (, ). Co-ordinates of A (, ) and (, ) of the line A. When it is reflected in x-axis then the image of A will be A and coordinates of A will be (, ) and will be (, ). A(, ) A(, ) (, ) (, ) 6. AC with points A (, ), (, ) and C (, ) is first reflected in x-axis to give A C and then this A C is reflected in y-axis to give A C. Find the co-ordinates of A, and C. Math Class VIII Question ank

15 In AC A (, ), (, ) and C (, ) Now, it is reflected in x-axis then A C is formed and A (, ), (,) and C (, ) Now it is reflected in y-axis and A C is formed and coordinate A (, ), (,) and C (, ) 7. A square PQRS with the vertices P (, ), Q (, ), R (, ) and S (, ) is first reflected in x-axis and the image so obtained is reflected in y-axis. Find the vertices of the final image so formed. The coordinates of the vertices of square PQRS are P (, ), Q (, ), R (, ) and S (, ) When it is reflected in x-axis, the image of PQRS will be P Q R S and their co-ordinates will be P (, ), Q (, ), R (, ) and S (, ) and when it is again reflected in y-axis, the image will be P Q R S and their co-ordinates will be P (, ), Q (, ), R (, ) and S (, ). 8. A rectangle ACD with its vertices at A (, ), (, ), C (, ) and D (, ) is rotated about the origin through 90 anticlockwise to take the new position PQRS. Find the co-ordinates of P, Q, R and S and draw the new figure. Given in rectangle ACD, A (, ), (, ), C (, ) and D (, ) is rotated through 90 anticlockwise then PQRS rectangle is formed, then P (, ), Q (, ), R (, ) and S (, ). Math Class VIII Question ank

16 6 R (, ) Q (, ) S (, ) 6 P (, ) 9. A quadrilateral ACD with its vertices at A (, ), (, ), C (, ) and D (, 0) is rotated through 90 clockwise to take the new position LMNQ. Find the coordinates of L, M, N and Q and draw the new figure. Given a quadrilateral ACD with its vertices A (, ), (, ), C (, ) and D (, 0) is rotated through 90 clockwise then quadrilateral LMNQ is formed. Then, coordinates of L (, ), M (, ), N (, ) and Q (0, ) N(, ) M(, ) 0 Q(0, ) L(, ) 0. A AC has its vertices at A (, 0), (, ) and C (, ). This triangle is rotated about the origin through 80 to take the position A C. Find the co-ordinates of A, and C. Show the new figure on the graph paper. Math Class VIII 6 Question ank

17 The triangle AC whose vertices are A (, 0), (, ) and C (, ) is rotated about the origin through 80, then the co-ordinates of the image of AC will be A C and co-ordinates will be A (, 0), (, ) and C (, ). A (, 0) 0 (, ) C (, ). Construct the image of AC under a rotation about the origin O through 80, the vertices of the triangle being at A (, ), (, ) and C (, ). The image of AC under rotation about the origin O through 80, will be A C. The co-ordinates of A will be (, ), of (, ) and C (, ). A (, ) x 0 (, ) y y C (, ) Math Class VIII 7 Question ank