Matrices Transformations

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Gerald McDowell
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1 Matrices Transformations

2 (a) A 7 On the grid, draw the image of (i) shape A after a reflection in the line =, [] (ii) shape A after an enlargement with scale factor, centre (, ), [] (iii) shape A after the transformation represented b the matri - c m. [] (b) Describe full the single transformation represented b the matri c m [] UCLES 8//M/J/ [Turn over

3 9 U 8 V 8 8 T (a) (i) Draw the image of triangle T after a reflection in the line =. [] (ii) Draw the image of triangle T after a rotation through 9 clockwise about (, ). [] (iii) Describe full the single transformation that maps triangle T onto triangle U [] (iv) Describe full the single transformation that maps triangle T onto triangle V [] (b) (i) Find the matri that represents the transformation in part (a)(i). f p [] (ii) Describe full the single transformation represented b the inverse of the matri in part (b)(i) [] UCLES 8//M/J/ [Turn over

4 8 7 A B (a) v = c - -8 m 8 (i) Draw the image of triangle A after the translation b vector v. [] (ii) Calculate v.... [] UCLES 8//O/N/

5 (b) (i) Describe full the single transformation that maps triangle A onto triangle B [] (ii) Find the matri that represents the transformation that maps triangle A onto triangle B. f p [] (iii) Calculate the determinant of the matri in part (b)(ii).... [] UCLES 8//O/N/ [Turn over

6 8 7 T 8 7 U W (a) On the grid, draw the image of - (i) triangle T after a translation b the vector e o, [] (ii) triangle T after a reflection in the line =. [] UCLES 8//O/N/

7 (b) Describe full the single transformation that maps triangle T onto triangle U. Answer(b) [] (c) (i) Describe full the single transformation that maps triangle T onto triangle W. Answer(c)(i) [] (ii) Find the matri that represents the transformation in part (c)(i). Answer(c)(ii) f p [] UCLES 8//O/N/ [Turn over

8 (a) For Eaminer s Use Q P 7 8 (i) Describe full the single transformation which maps shape P onto shape Q. Answer(a)(i)... [] (ii) On the grid above, draw the image of shape P after reflection in the line =. [] (iii) On the grid above, draw the image of shape P under the transformation represented b the matri - e o. [] UCLES 8//M/J/

9 (ii) Find the ratio AL : AN in its simplest form. 9 Answer(b)(ii)... :... [] (c) A 7 B (i) On the grid, draw the image of triangle A after the transformation represented b the -. matri f p. [] -. (ii) Find the matri which represents the transformation that maps triangle A onto triangle B. Answer(c)(ii) f p [] Question is printed on the net page. UCLES 8//M/J/ [Turn over

10 9 (a) N = - f p Describe full the single transformation represented b N. Answer(a) [] (b) Find the matri which represents the single transformation that maps triangle A onto triangle B. 7 A B Answer(b) f p [] (c) On the grid, draw the image of triangle A under a stretch, factor, with the -ais invariant. [] Permission to reproduce items where third-part owned material protected b copright is included has been sought and cleared where possible. Ever reasonable effort has been made b the publisher (UCLES) to trace copright holders, but if an items requiring clearance have unwittingl been included the publisher will be pleased to make amends at the earliest possible opportunit. Cambridge International Eaminations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of Universit of Cambridge Local Eaminations Sndicate (UCLES), which is itself a department of the Universit of Cambridge. UCLES 8//O/N/

11 7 C A B 7 (a) Draw the image of (i) - shape A after a translation b f p, [] (ii) shape A after a rotation through 8 about the point (, ), [] (iii) shape A after the transformation represented b the matri f p. [] - (b) Describe full the single transformation that maps shape A onto shape B. Answer(b) [] (c) Find the matri which represents the transformation that maps shape A onto shape C. Answer(c) f p [] UCLES 8//M/J/

12 8 7 B A (a) Describe full the single transformation that maps triangle A onto triangle B. Answer(a) [] UCLES 8//O/N/

13 7 (b) On the grid, draw the image of (i) triangle A after a reflection in the line =, [] (ii) triangle A after a rotation about the origin through 7 anticlockwise, [] - (iii) triangle A after a translation b the vector e o. - [] (c) M is the matri that represents the transformation in part (b)(ii). (i) Find M. Answer(c)(i) M = f p [] (ii) Describe full the single transformation represented b M, the inverse of M. Answer(c)(ii) [] UCLES 8//O/N/ [Turn over

14 7 (p, q) is the image of the point (, ) under this combined transformation. p f p = q f - p f p + f p (a) Draw the image of the triangle under the combined transformation. For Eaminer s Use [] (b) Describe full the single transformation represented b - f p. Answer (b)... [] UCLES 8//O/N/

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certifi cate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certifi cate of Secondary Education *2635490223* MATHEMATICS 0580/42 Paper 4 (Extended) October/November 2013 2 hours 30 minutes