9 MATRICES AND TRANSFORMATIONS

Transcription

1 9 MTRIES ND TRNSFORMTIONS TSK 9.. ¼ a þ b c d e det f g h. ¼ p and ¼ a Find the value of p if det ¼. b Find the value of p if det ¼. c If p ¼, find.. M ¼ a M b X c X.IfMX ¼ 7. Epress as a single matri: 8, find: TSK 9.. Use translation vectors to describe the following translations. a Dto b EtoD c to d EtoF e DtoH f HtoF g Eto h EtoG i GtoD j Fto E G D F H Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

2 Matrices and transformations. op the grid opposite and draw shape as shown. Translate shape b each of the translation vectors shown below: a b c d e label new shape. label new shape. label new shape D. label new shape E. Use a translation vector to describe the translation that moves shape D to E. TSK 9.. For each pair of shapes below, write down the name of the line of reflection. a to b to c tod d DtoE e EtoF D E F. op the grid and shape opposite. a Reflect rectangle in the line =. Label the image. b Draw the line =. c Reflect rectangle in the line =. Label the image. d Write down the translation vector which transforms rectangle onto rectangle. = Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

3 Matrices and transformations. a Draw an -ais from to and a -ais from to. b Draw a triangle P with vertices (, ), (, ) and (, ). c Reflect triangle P in the line =. Label the image Q. d Reflect triangle Q in the line + =. Label the image R. e Reflect triangle R in the line =. Label the image S. f Reflect triangle S in the -ais. Label the image T. g Describe full the transformation which maps T back onto P.. a Draw an -ais from to and a -ais from to. b Draw an -shape with vertices (, ), (, ), (, ), (, ), (, ) and (, ). c Translate shape through. Label the image. d Ref lect shape in the line =. Label the image. e Translate shape through. Label the image D. f Shape D is reflected back onto shape. Write down the equation of the line of reflection. TSK 9. You ma use tracing paper. For each question, draw the shape and the centre of rotation (). Rotate the image as indicated and draw the image clockwise 9 anticlockwise 8 9 anticlockwise. Find the co-ordinates of the centres of the following rotations: a shape onto shape b shape onto shape c shape onto shape D 8 7 D 7 8 Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

4 Matrices and transformations. a Draw the ais from to. Draw the ais from to7. Draw rectangle with vertices at (, ), (, ), (, ), (, ). b Rotate rectangle 9 clockwise about (, ). Label the image. c Rotate rectangle 9 clockwise about (, ). Label the image. d Rotate rectangle 9 clockwise about the origin. Label the image D. e Rotate rectangle D 9 anticlockwise about (, ). Label the image E. f Describe full the translation which transforms rectangle onto rectangle E. 7. Describe full the rotation which transforms: a triangle onto triangle b triangle onto triangle D c triangle onto triangle D TSK 9. For Questions and, draw the grid and the two shapes then draw broken lines through pairs of points in the new shape and the old shape. Describe full the enlargement which transforms shape onto shape... 7 Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

5 Matrices and transformations For Questions to, cop the diagram and then draw an enlargement using the scale factor and centre of enlargement () given. Leave room for the enlargement!... scale factor scale factor scale factor. a Draw an -ais from 7 to 7 and a -ais from 7 to7. b Draw a rectangle P with vertices at (, ), (, ), (, ) and (, ). c Enlarge rectangle P b scale factor about (, ). Label the image Q. 8 d Translate rectangle Q through. Label the image R. e Enlarge rectangle R b scale factor about (, 7). Label the image S. f Enlarge rectangle S b scale factor about (, ). Label the image T. g Describe full the transformation which maps T onto P. TSK 9.. a Draw an -ais from to and a -ais from to. b Draw an -shape with vertices at (, ), (, ), (, ), (, ), (, ) and (, ). c Enlarge the shape b a scale factor of about (, ). d If P is the verte (, ) in the original shape, write down the co-ordinates of the corresponding verte in the new shape. For Questions and, describe full the enlargement which transforms shape onto shape (draw the grid and shape if necessar) Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

6 . a Draw an -ais from to and a -ais from to. b Draw a triangle with vertices at (, ), (, ) and (, ). c Enlarge triangle b a scale factor of about the origin. Label the image. d Enlarge triangle b a scale factor of about (, ). Label the image. e Describe full the transformation which maps onto. Matrices and transformations TSK 9.7. Describe full the transformation which moves: a triangle onto triangle b triangle onto triangle c triangle onto triangle D d triangle D onto triangle E e triangle D onto triangle F F. a Draw the -ais from to. Draw the -ais from to. Draw shape with vertices at (, ), (, ), (, ), (, ). b Enlarge shape b scale factor about the origin. Label the image. c Reflect shape in the line =. Label the image. d Rotate shape 9 anticlockwise about (, ). Label the image D. e Translate shape D through. Label the image E. f Rotate shape E 9 clockwise about (, ). Label the image F. g Describe full the transformation that would move shape F onto shape.. a Draw an -ais from 7 to 7 and a -ais from 7 to7. b Draw rectangle P with vertices at (, ), (, ), (, ) and (, ). c Enlarge rectangle P b a scale factor of about the origin. Label the image Q. d Reflect rectangle Q in the line + =. Label the image R. e Rotate rectangle R 9 clockwise about the origin. Label the image S. f Translate rectangle S through. Label the image T. g Describe full the transformation which maps T onto Q. D E Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

7 Matrices and transformations 7 TSK 9.8. The matri represents the transformation X. a Find the image of (, ) under X. b Find the image of (, ) under X. c Find the image of the triangle with vertices (, ), (, ) and (, ) under X. d Describe the transformation represented b X.. Write down matrices representing the following transformations: a Enlargement scale factor centre (, ). b Reflection in the line ¼. c Reflection in the line ¼. d Rotation of 8, centre (, ).. Plot the rectangle D on graph paper where (, ), (, ), (, ) and D(, ). Find and draw the image of D under the following transformations: a b c d e For each of parts a to d, describe the transformation full and write down the invariant line.. Write down the transformations represented b the following matrices: a b c d e. The rectangle D has coordinates (, ), (, ), (, ) and D(, ). a Draw the rectangle on graph paper. b Draw the image D of D under the transformation. c d Draw the image of D under the transformation Write down the matri represented b the combined transformations.. Ó OUP: this ma be reproduced for class use solel for the purchaser s institute

8 Matrices and transformations 8. Write down the matrices representing the following transformations: a Stretch parallel to the -ais, factor. b Stretch parallel to the -ais, factor.. c Shear, invariant line O, factor. d Shear, invariant line O, factor e Enlargement scale factor, centre (, ) f Two-wa stretch, factor parallel to the -ais and factor parallel to the -ais. Ó OUP: this ma be reproduced for class use solel for the purchaser s institute