8.4.4f-Combined-enlargements---clicker---TES.pptx

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1. Ex1 Work out the scale factor that enlarges rectangle A onto rectangle B. Solution Ex2 Here are two similar right-angled triangles. Write the ratio of side to side .   Solution A B 9 3 9 3   Scale factor 3       3 9 Ratio   3 9   1 3   3   Divide equivalent lengths. Divide equivalent lengths.

2. Q1 Find the scale factor the enlarges A onto each of the other rectangles. Solution Q2 Find the scale factor the enlarges B onto each of the other triangles. Solution A B Scale factor 2 Scale factor 5 Scale factor 2 Scale factor 3½ 4 2 4 2   2   10 2   5   10 12 4 12 4   3   Scale factor 3 14 14 4   3.5   8 8 4   2  

3. C Ex3 Enlarge shape A by a scale factor of 2 and label its image B. Solution Ex4 Enlarge shape C by a scale factor of 3 and label its image D. Solution A B D Multiply the lengths by the scale factor. Multiply the lengths by the scale factor. Join the points for the diagonal.

4. Q3 Enlarge C by a scale factor 4. Solution Q4 Enlarge D by a scale factor 6. Solution C D 4 2 16 8 2 2 1 1 12 12 6 6

5. Ex5 Give the coordinates of the centre of enlargement. Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2   (-8,-7) Ex6 Give the coordinates of the centre of enlargement. Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2   (-5,5) Draw straight lines through corresponding vertices. The intersection is the centre of enlargement. Draw straight lines through corresponding vertices. The intersection is the centre of enlargement.

6. (-4,-3) 2 Ex7 Describe fully the single transformation that maps P onto Q. Solution Ex8 Describe fully the single transformation that maps S onto T. Solution -4 -3 -2 -1 1 2 3 4 5   -7 -6 -5 -4 -3 -2 -1 1 2 3 4   5 6 7 -4 -3 -2 -1 1 2 3 4 5   -7 -6 -5 -4 -3 -2 -1 1 2 3 4   5 6 7 Q P (2,0) Enlargement, scale factor __ , centre _____ 2 (2,0) Enlargement, scale factor __ , centre ______ (-4,-3) S T 4 2   2   It’s not always necessary to draw through every vertex . 4 2   2  

7. Q9 Describe fully the single transformation that maps A onto B. Solution Q10 Describe fully the single transformation that maps C onto D. Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 B A C D     Enlargement Scale factor 3 Centre (2,5) Enlargement Scale factor 3 Centre (6,5)

8. Q11 Describe fully the single transformation that maps I onto J. Solution Q12 Describe fully the single transformation that maps K onto L. Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 L K I J   Enlargement Scale factor 3 Centre (8,3)   Enlargement Scale factor 4 Centre (-8,6)

9. Ex9 On the grid, enlarge the shape, scale factor 2, centred at (-6,8). Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 Identify the centre and enlarge as normal. D5 R2   D10 R4   D7 R2   D14 R4   R5 D5   R10 D10   R5 D7   R10 D14   Ex10 On the grid, enlarge the shape, scale factor 4, centre (4,5). Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 L2 D0   L8 D0   D2 L0   D8 L0   L2 D2   L8 D8   Identify the centre and enlarge as normal.

10. Q13 On the grid, enlarge the shape by a: [a] scale factor 3, centre (7,1) [b] scale factor 2, centre (-1,7) Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 -14 -12 -10 -16 12 14 16 10 L4 U2   L12 U6   L6 U1   L18 U3   L3 U0   L9 U0   L4 U0   L12 U0   D5 R2   D10 R4   D6 R4   D12 R8   R5 D6   R10 D12   R4 D4   R8 D8  

11. Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 -14 -12 -10 -16 12 14 16 10 Q12 On the grid, enlarge the shape by a: [a] scale factor 2, centre (8,8) [b] scale factor 2, centre (-2,3) L5 D4   L10 D8   L6 D5   L12 D10   L6 D6   L12 D12   D6 L4   D12 L8   D4 L4   D8 L8   U1 R5   U2 R10   R4 U0   R8 U0   D1 R4   D2 R8   D1 R6   D2 R12   U1 R6   U2 R12  

12. Q15 Describe the single transformation that maps: 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 -14 -12 -10 -16 12 14 16 10 18 20 22 24 -18 -20 -22 -24 Solution [a] P onto Q. [b] Q onto P. [c] S onto R. [d] R onto S. P Q R Enlargement [sf 2] centre (-9,3) Enlargement [sf 2] centre (5,-6) Enlargement [sf ½] centre (-9,3) Enlargement [sf ½] centre (5,-6) S

13. Q16 Describe the single transformation that maps: 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 -14 -12 -10 -16 12 14 16 10 18 20 22 24 -18 -20 -22 -24 Solution [a] T onto U. [b] U onto T. [c] W onto U. [d] V onto W. Enlargement [sf 2] centre (-21,6) Enlargement [sf 4] centre (-9,0) Enlargement [sf ½] centre (-21,6) Enlargement [sf ⅙ ] centre (-9,3) T U V W