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

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1. To enlarge a shape by a scale factor , we first describe the movement from the centre to a point on the shape . Then we multiply the movement starting from the centre using the given scale factor . U2 R3   U4 R6   Scale factor 2 Ex1 On the grid, enlarge the shape, scale factor 3, centre A. Solution U3 R3   U9 R9   R3 U0   R9 U0   R6 U1   R18 U3   A Describe movement from centre to a point . Multiply by the scale factor. Repeat for the other points. Join the points to finish the enlargement.

2. Ex2 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   Ex3 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.

3. Q1 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  

4. Q2 Enlarge shape A, scale factor ⅓ , centred at (-12,1) and label the image B. Then enlarge shape B, scale factor 2, centred at (-5,5) and label the image C. What is the scale factor used to enlarge shape A to shape C? 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 18 20 22 24 -18 -20 -22 -24 A U6 R24   U2 R8   U3 R15   U1 R5   R15 U0   R5 U0   R24 U0   R8 U0   B R1 D2   R2 D4   L2 D3   L4 D6   L2 D4   L4 D8   R1 D4   R2 D8   C A scale factor ⅔ enlarges shape A to shape C.

5. Q3 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] R onto S. [d] P onto R. P Q R Enlargement [sf 2] centre (-9,3) Enlargement [sf ½] centre (5,-6) Enlargement [sf ½] centre (-9,3) Enlargement [sf 2] centre (1,8) S

6. Q4 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

7. Ex4 On the grid, enlarge the shape by scale factor -2, centre A. Solution Describe movement from centre to a point . A U2 R3   D4 L6   Reverse the movement using the scale factor. Effect of negative: Up Down Left Right   R2 L4 Repeat for the other points. R4 L8 Join the points to finish the enlargement. Ex5 On the grid, enlarge the shape, scale factor -2, centre C. Solution C Describe movement from centre to a point . U2 R3   D4 L6   Reverse the movement using the scale factor. Effect of negative: Up Down Left Right   Repeat for the other points. D1 R4   U2 L8   U1 R1   D2 L2   Join the points to finish the enlargement.

8. Ex6 On the grid, enlarge the shape by scale factor -2, centred at the origin. Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 D1 L2   U2 R4   D2 L3   U4 R6   D2 L1   U4 R2   D4 L2   U8 R4   Ex7 On the grid, enlarge the shape by scale factor - ½ , centre (3,-4). Solution 2 4 6 8     -8 -6 -4 -2 -6 -4 -2 -8 4 6 8 2 U10 L8   D5 R4   U6 L2   D3 R1   U4 L2   D2 R1   L4 R2

9. A Q5 On the grid, enlarge the shape by scale factor -3, centre A. Solution Q6 On the grid, enlarge the shape by scale factor - ½ , centre B. Solution U4 R5   D12 L15   U1 R2   D3 L6   D1 R6   U3 L18   B U8 D4 R8 U6   L4 D3   R8 U2   L4 D1   R2 L1

10. Q7 On the grid, enlarge the shape by a: [a] scale factor -2, centre (0,0) [b] scale factor -1, centre (6,-2) 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 U2 R1   D4 L2   U3 R3   D6 L6   U1 R3   D2 L6   U1 R4   D2 L8   U5 L3   D5 R3   U4 L5   D4 R5   U3 L3   D3 R3   U3 L2   D3 R2  

11. Q8 On the grid, enlarge the shape by a: [a] scale factor -2, centre (0,1) [b] scale factor -3, centre (-1,3) 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 U3 R4   D6 L8   U3 R3   D6 L6   U2 R2   D4 L4   R2 U1   L4 D2   R4 U1   L8 D2   U1 R5   D3 L15   U1 R4   D3 L12   R3 L9 D1 R3   U3 L9   D1 R5   U3 L15  

12. Q9 Enlarge shape A, scale factor -2, centred at (-2,-6) and label the image B. Then enlarge shape B, scale factor -3, centred at (-3,-2) and label the image C. What is the scale factor used to enlarge shape A to shape C? 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 U1 R10   D2 L20   R7 L14 A D1 R7   U2 L14   D1 R10   U2 L20   B D1 L4   U2 R8   D1 L10   U2 R20   D3 L4   U6 R8   D5 L10   U10 R20   C A scale factor 4 enlarges shape A to shape C.

13. Q10 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] R onto P. [d] P onto R. P Q R Enlargement [sf -1] centre (-10,4) Enlargement [sf -¼] centre (-13,5) Enlargement [sf -1] centre (-10,4) Enlargement [sf -4] centre (-13,5)

14. Q11 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] U onto V. [d] T onto V. Enlargement [sf -2] centre (-8,3) Enlargement [sf – 3 ⁄ 2 ] centre (0,1) Enlargement [sf -½] centre (-8,3) Enlargement [sf -3] centre (-9,2.5) T U V