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60 38 0 0 61 130 61 131 60 37 0 0 61 103 61 107 60 36 0 0 61 99 61 100 61 101 60 1 0 0 61 63 61 64 61 65 61 67 60 2 0 0 61 59 61 60 61 61 61 62 60 3 0 0 61 55 61 56 61 57 61 58 60 4 0 0 61 51 61 52 61 53 61 54 60 5 0 0 61 49 61 50 60 6 0 0 61 46 61 47 60 8 0 0 61 39 61 40 60 9 0 -30 61 6 61 7 61 8 60 10 0 0 61 6 61 7 60 17 0 0 61 13 61 12 13 0 -1150 1488 0 J:\Lessons\A-Level\Further_maths\Further_Pure_1\Matrices\Transformations\Reflections.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 4 0 0 -1 -1 -1 0 65536  0 0 0 0 5 0 1557 0 0 0 0 0 4 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 ETRotate 0 0 FF000000 00FF0000 nyn 00 0 yn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 320 430 -299 -381 0 yyyyyg 326 -360 Easiteach 4 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 0 16 0 36800 4 55 -15 0 1 0 23 5 0 00000429 15 811 984 -297 -379 0 yyyyyf 817 -358 Easiteach 8 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 sin 2 16 0 62000 8 55 -15 0 1 0 23 5 0 00000371 15 808 969 -353 -435 0 yyyyyf 814 -414 Easiteach 6 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 -cos 2 16 0 57200 6 55 -15 0 1 0 23 18 0 00000079 23 5 0 00000369 23 18 1 00000079 15 949 1013 -297 -379 0 yyyyye 955 -358 Easiteach 2 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 33 959 981 -326 -353 0 nyyyye Outline 62 0 5 n 0 n 16777216 0 0 0 0 0  43 5 00000005 43 2 00000079 43 1 00000000 15 951 1015 -353 -435 0 yyyyye 957 -414 Easiteach 2 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 33 961 983 -382 -409 0 nyyyye Outline 62 0 7 n 0 n 16777216 0 0 0 0 0 uttttttttttttttttttt 43 5 00000005 43 2 00000079 43 1 00000000 15 733 797 -294 -376 0 yyyyyd 739 -355 Easiteach 2 8 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 18 301 323 -301 -330 0 yyyyyd Outline 321 -315 303 -316 9 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 289 317 -314 -427 0 yyyyyd Outline 303 -316 303 -425 10 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 33 743 765 -323 -350 0 nyyyyd Outline 62 0 11 n 0 n 16777216 0 0 0 0 0  43 5 00000005 43 2 00000079 43 1 00000000 15 722 786 -356 -438 0 yyyyyd 728 -417 Easiteach 2 12 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 33 732 754 -385 -412 0 nyyyyd Outline 62 0 13 n 0 n 16777216 0 0 0 0 0 rqqqqqqqqqqqqqqqqqqq 43 5 00000005 43 2 00000079 43 1 00000000 18 289 317 -411 -439 0 yyyyyd Outline 303 -425 303 -425 14 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 301 321 -411 -439 0 yyyyyd Outline 303 -425 319 -425 15 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 583 605 -303 -332 0 yyyyyc Outline 603 -317 585 -318 16 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 571 599 -316 -429 0 yyyyyc Outline 585 -318 585 -427 17 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 571 599 -413 -441 0 yyyyyc Outline 585 -427 585 -427 18 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 583 603 -413 -441 0 yyyyyc Outline 585 -427 601 -427 19 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 986 1006 -300 -329 0 yyyyyb Outline 1004 -314 988 -315 20 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 990 1018 -300 -328 0 yyyyyb Outline 1004 -314 1004 -314 21 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 990 1019 -312 -425 0 yyyyyb Outline 1005 -423 1004 -314 22 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 477 576 -348 -385 0 yyyyyb Outline 481 -365 572 -367 23 n 0 n 0 0 0 24 6 00000001 24 5 00000005 24 2 00000079 18 985 1007 -409 -439 0 yyyyyb Outline 987 -425 1005 -423 24 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 414 434 -303 -332 0 yyyyya Outline 432 -317 416 -318 25 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 418 446 -303 -331 0 yyyyya Outline 432 -317 432 -317 26 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 418 447 -315 -428 0 yyyyya Outline 433 -426 432 -317 27 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 413 435 -412 -442 0 yyyyya Outline 415 -428 433 -426 28 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 15 179 1079 -83 -165 0 yyyyy` 185 -144 Easiteach 37 29 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 If we put our results together we get 16 0 352800 37 55 -15 0 1 0 23 5 0 000004D8 15 612 752 -294 -436 0 yyyyy` 618 -355 Easiteach 11 30 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 cos 2 sin 2 16 0 48800 5 55 -15 0 1 0 16 6 44000 5 55 -15 0 1 0 23 18 0 00000079 23 5 0 00000080 18 539 760 -433 -626 0 yyyyy` Outline 559 -606 740 -453 31 n 0 n 0 0 0 24 6 00000001 24 5 00000014 24 2 00000079 24 0 4888ff00 15 266 1270 -592 -734 0 yyyyy` 272 -653 Easiteach 82 32 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 This is our transformation matrix for any reflection in a line through the origin. 16 0 394400 41 55 -15 0 1 0 16 42 352000 40 55 -15 0 0 0 23 4 0 FF702800 23 5 0 0000048A 15 319 429 -358 -440 0 yyyay_ 325 -419 Easiteach 4 34 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 1 16 0 36800 4 55 -15 0 1 0 23 5 0 00000425 19 615 991 -313 -429 0 yyyyy^ Outline 33 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffd7eb00 15 279 1443 -791 -933 0 yyyyy^ 285 -852 Easiteach 57 49 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 The general equation of a line through the origin will be 16 0 458400 49 55 -15 0 1 0 16 50 59200 7 55 -15 0 0 0 23 4 0 FF702800 23 5 0 00000486 15 454 705 -849 -931 0 yyyyy^ 460 -910 Easiteach 11 50 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 y = x tan 16 0 93200 11 55 -15 0 1 0 23 4 0 3800A800 23 5 0 00000403 15 449 513 -926 -1008 0 yyyyy^ 455 -987 Easiteach 2 51 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 4 0 FF702800 23 5 0 000002C0 33 459 481 -955 -982 0 nyyyy^ Outline 62 0 52 n 0 n 16777216 0 0 0 0 0 87777777777777777777 43 5 00000005 43 2 00000079 43 1 ff702800 43 0 ff702800 15 665 729 -852 -934 0 yyyyy] 671 -913 Easiteach 2 64 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 4 0 3800A800 23 5 0 000002C0 33 675 697 -881 -908 0 nyyyy] Outline 62 0 65 n 0 n 16777216 0 0 0 0 0  43 5 00000005 43 2 00000079 43 1 ff702800 43 0 3800a800 15 291 1190 -924 -1006 0 yyyyy] 297 -985 Easiteach 38 59 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 where is the angle made with x-axis 16 0 352400 38 55 -15 0 1 0 23 4 0 FF702800 23 5 0 0000047A 60 53 0 0 61 64 61 65 60 52 0 0 61 51 61 52 60 18 0 0 61 8 61 11 60 19 0 0 61 12 61 13 60 20 0 0 61 25 61 26 61 27 61 28 60 21 0 0 61 20 61 21 61 22 61 24 60 22 0 0 61 16 61 17 61 18 61 19 60 23 0 0 61 9 61 10 61 14 61 15 60 24 0 0 61 6 61 7 60 25 0 0 61 4 61 5 13 0 -1150 1488 0 J:\Lessons\A-Level\Further_maths\Further_Pure_1\Matrices\Transformations\Reflections.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 2 0 0 -1 -1 -1 0 65536  0 0 0 0 4 0 1557 0 0 0 0 0 6 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 ETRotate 0 0 FF000000 00FF0000 nyn 00 0 yn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 18 106 151 -141 -759 0 yyyyyg Outline 129 -749 128 -151 1 n 0 n 0 0 0 24 6 00000001 24 5 0000000a 24 2 00000079 18 36 735 -656 -701 0 yyyyyg Outline 46 -679 725 -678 2 n 0 n 0 0 0 24 6 00000001 24 5 0000000a 24 2 00000079 18 126 444 -347 -681 0 yyyyyf Outline 131 -676 439 -352 3 n 0 n 0 0 0 24 5 0000000a 24 2 00000079 24 0 3800a800 18 422 453 -354 -681 0 yyyyyf Outline 436 -356 439 -679 4 n 0 n 0 0 0 24 2 00000079 24 0 d070ff00 24 5 00000005 18 124 552 -662 -697 0 yyyyyf Outline 129 -680 547 -679 5 n 0 n 0 0 0 24 5 0000000a 24 2 00000079 24 0 3800a800 33 421 448 -338 -371 0 nyyyye Outline 88 0 6 n 0 n 0 0 0 0 0 0  43 0 0000ff00 43 5 0000000a 33 424 443 -339 -378 0 nyyyye Outline 106 0 7 n 0 n 0 0 0 0 0 0  43 0 0000ff00 43 5 0000000a 33 535 552 -666 -690 0 nyyyye Outline 61 0 8 n 0 n 0 0 0 0 0 0 c`__^]\Z Y X!V"V#V#U$U$T$S$R%R%Q 43 0 0000ff00 43 5 0000000a 33 533 550 -663 -696 0 nyyyyd Outline 88 0 9 n 0 n 0 0 0 0 0 0 KKKKMNNOQRSTUVX Y Z \ ] ^!_!`!a"a"c"d#d#e#f 43 0 0000ff00 43 5 0000000a 15 473 555 -295 -377 0 yyyyyc 479 -356 Easiteach 2 11 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 M' 16 0 25600 2 55 -15 0 1 0 23 5 0 00000321 23 4 0 FF702800 33 284 315 -619 -677 0 nyyyyc Outline 169 0 12 n 0 n 0 0 0 0 0 0 8_8^8^8_8`8b8c8d8e8g8g8i8j8k8l8n8o8p7p7q7r7t7u7v6v6y6z5{5|5}4}4~433110//..,+*)(''%$#!! 43 5 0000000a 33 260 291 -560 -618 0 nyyyyb Outline 169 0 85 n 0 n 0 0 0 0 0 0                         43 5 0000000a 33 283 314 -604 -635 0 nyyyyb Outline 67 0 13 n 0 n 0 0 0 0 0 0   "#$&'()*+-./0234567 43 5 0000000a 33 269 299 -618 -644 0 nyyyyb Outline 49 0 14 n 0 n 0 0 0 0 0 0  43 5 0000000a 15 225 274 -416 -498 0 yyyyya 231 -477 Easiteach 1 15 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 16 0 12400 1 55 -15 0 1 0 23 5 0 00000419 23 4 0 FF702800 33 255 286 -540 -571 0 nyyyya Outline 67 0 83 n 0 n 0 0 0 0 0 0      43 5 0000000a 33 240 270 -554 -580 0 nyyyya Outline 49 0 84 n 0 n 0 0 0 0 0 0  43 5 0000000a 15 276 320 -677 -759 0 yyyyya 282 -738 Easiteach 1 16 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 a 16 0 10400 1 55 -15 0 1 0 23 5 0 000003E6 15 457 505 -460 -542 0 yyyyy` 463 -521 Easiteach 1 17 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 b 16 0 12000 1 55 -15 0 1 0 23 5 0 00000331 15 246 295 -608 -690 0 yyyyy` 252 -669 Easiteach 1 18 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 12400 1 55 -15 0 1 0 23 4 0 FF702800 23 5 0 000004B4 33 257 279 -636 -667 0 nyyyy` Outline 52 0 19 n 0 n 16777216 0 0 0 0 0  dt s sssss s s s sxsks]sOs5s's 43 0 ff702800 43 7 00000005 43 5 0000000a 15 879 984 -202 -284 0 yyyay_ 885 -263 Easiteach 4 20 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 = 16 0 34800 4 55 -15 0 1 0 23 5 0 000004B4 15 773 913 -202 -284 0 yyyyy^ 779 -263 Easiteach 5 21 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 cos2 16 0 48800 5 55 -15 0 1 0 23 18 0 00000079 23 5 0 0000028F 33 887 910 -229 -261 0 nyyyy^ Outline 52 0 22 n 0 n 16777216 0 0 0 0 0 z z z { } ~            43 5 0000000a 15 970 1014 -172 -254 0 yyyyy] 976 -233 Easiteach 1 23 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 a 16 0 10400 1 55 -15 0 1 0 23 5 0 000001B7 18 964 1017 -228 -256 0 yyyyy] Outline 966 -242 1015 -242 24 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 15 975 1024 -232 -314 0 yyyay] 981 -293 Easiteach 1 25 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 16 0 12400 1 55 -15 0 1 0 23 5 0 000001AA 15 1149 1325 -202 -284 0 yyyyy\ 1155 -263 Easiteach 7 26 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 a = cos 16 0 63200 7 55 -15 0 1 0 23 5 0 0000014C 23 18 4 00000079 15 1313 1408 -205 -287 0 yyyay\ 1319 -266 Easiteach 3 27 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 20 16 0 30800 3 55 -15 0 1 0 23 5 0 000004B4 33 1354 1377 -232 -264 0 nyyyy\ Outline 52 0 28 n 0 n 16777216 0 0 0 0 0 M MMNPQRSTUWXYZ[\^ 43 5 0000000a 15 783 911 -430 -512 0 yyyyy\ 789 -491 Easiteach 5 29 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 sin2 16 0 44000 5 55 -15 0 1 0 23 5 0 0000028F 15 879 984 -432 -514 0 yyyay\ 885 -493 Easiteach 4 30 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 = 16 0 34800 4 55 -15 0 1 0 23 5 0 000004B4 15 970 1018 -402 -484 0 yyyyy[ 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21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100