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Kata Pengantar ...................................................................................................................................... i Daftar Isi ............................................................................................................................................... ii Bab 3 Transformasi Geometri ............................................................................................................... 1 A. Kompetensi Dasar....................................................................................................................... 1 B. Peta Konsep................................................................................................................................ 1 C. Sejarah........................................................................................................................................ 2 D. Transformasi Geometri............................................................................................................... 2 1. Pengertian Transformasi ....................................................................................................... 3 2. Pengertian Transformasi Geometri ....................................................................................... 5 3. Jenis Transformasi Geometri................................................................................................. 6 E. Refleksi ....................................................................................................................................... 6 1. Pengertian Refleksi ............................................................................................................... 8 2. Rumus Refleksi...................................................................................................................... 9 3. Kuis 1................................................................................................................................... 25 F. Translasi ..................................................................................................................................... 32 1. Pengertian Translasi............................................................................................................ 34 2. Rumus Translasi .................................................................................................................. 35 3. Kuis 2................................................................................................................................... 40 G. Dilatasi........................................................................................................................................ 45 1. Pengertian Dilatasi .............................................................................................................. 47 2. Rumus Dilatasi..................................................................................................................... 48 3. Kuis 3................................................................................................................................... 51 H. Rotasi.......................................................................................................................................... 56 1. Pengertian Rotasi ................................................................................................................ 58 2. Rumus Rotasi ...................................................................................................................... 59 3. Kuis 4................................................................................................................................... 71 I. POSTES...................................................................................................................................... 76 J. RANGKUMAN............................................................................................................................ 81 1. TRANSFORMASI GEOMETRI ................................................................................................ 81 2. REFLEKSI.............................................................................................................................. 82 3. TRANSLASI........................................................................................................................... 83 4. DILATASI.............................................................................................................................. 83 5. ROTASI ................................................................................................................................ 84 Daftar Pustaka .................................................................................................................................... 86 ii
Transformasi Geometri Sistem Koordinat (Materi Prasyarat) Refleksi Translasi Dilatasi Rotasi (Pencerminan) (Pergeseran) (Perputaran) (Perbesaran /Perkecilan) 1
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Ayo kita simak dulu ya video berikut Tampilkan video di sini https://www.youtube.com/watch?v=U6jbvHVqvRg 3
وََلقَدْ خَلَقنَا ٱْلِن ٰسََنَْ مِن سَُٰلََلةْ مِن طِينْ ُثْم جَعَلٰنََُْه ُنطفَةْ فِى قَرَاْر مكِيْن ُثمْ خََلقنَا ٱلُنّطفََْة عَلَقَْة فَخََلقنَا ٱلعََلقََْة ُمضغَْة فَخَلَقنَا ٱلمُضغََةْ عِٰظََما فَكَسَوَنا ٱلعِٰظََمََْلحما ُثْم أَنشَأََٰنُْه خَلقا َءاخَْرَ ْۚ فَتَبَارَْكَ ٱّلْلُأَحسَْنُ ٱل ٰخََلِقِينَْ 4
Materi Prasyarat Gambar di samping merupakan Sistem Koordinat bidang koordinat yang terdiri dari sumbu X untuk garis horizontal yang Y disebut absis serta sumbu Y untuk garis vertikal yang disebut ordinat. A• •D • Mari kita tuliskan titik koordinat yang X ada di gambar tersebut. B Titik A(3, 5) C• Titik B(5, -1) Gambar 4 Titik C(0, -6) Titik D(-2, 0) 5
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َٰٰٓياَُّيَها الذِيْنَ ٰاََمنُوا اتقُوا اّلْٰلَوَلتَنظُْر َنفسْ ما قَدَمْت ِلغَدْ وَاتقُوا اّلٰلَْۚاِنْ اّلْٰلَخَبِيْر ۚبِمَا َتعمَُلوْنَ 7
Objek Bayangan C jarak E jarak R M I N So, how about the reflection? 8
Y •A X B• 0 •C • • • 9
•• •• •• •• •• •• Y 6 satuan 6 satuan cermin A’(-6, 6)• •A(6, 6) 0 X B(-4, -3)• 4 satuan 4 satuan •B’(4, -3) •C(2, -6) 10
✓ My ✓ My My My 11
My My My 12
✓ Mx ✓ Mx Mx Mx Mx Mx 13
My Mx E(-7, 8) Y cermin y=x • D’(2, 5) F(-6, 1) • • •D(5, 2) 0X • E’(8, -7) 14
✓ y=x ✓ y=x y=x y=x y=x 15
y=x y=x Mx cermin Y y=-x • S’(2, 3) U(-9, 4) • 0 X • T(8,•-2) S(-3, -2) T’(•2, -8) 16
✓ y=-x ✓ y=-x y=-x y=-x y=-x 17
y=-x y = - x My Mx Y x = 3 cermin D(-1, 7) • • D’(7, 7) 4 satuan 4 satuan • E(-8, 3) 0X 6 satuan 6 satuan C’(-3, -5)• • C(9, -5) 18
✓ x=3 ✓ x= 3 x=h x=3 19
x=-5 x=-5 x=-4 Mx y = x 20
Y K’(4, 9) • J(-6, 7) 5 satuan • cermin 3 satuan y=4 3 satuan 5 satuan X • J’(-6, 1) • 0 K(4, -1) L(-9, -5) • ✓ y=4 ✓ y= 4 21
y=k y=4 y=6 y=6 y=-8 y = -x x=3 22
Y •D(-3, 7) 7 • C(1, 7) •A(-3, 4) 6 5 4 •B(1, 4) 3 2 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 1112 X -1 -2 •A’(-3, -4) • •-3 B’’(7, -4) -4 B’(1, -4) • A’’(11, -4) -5 •D’(-3, -7) •-6 C’(1, -7) •C’’(7, -7) • D’’(11, -7) -7 x=4 Mx x = 4 Mx x = 4 23
Mx x = 4 Mx x = 4 24
https://qrgo.page.link/7yhUf Ssstt….kini saatnya kita mengerjakan kuisnya ya 25
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x=-4 x=-4 x=-4 x=-4 27
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Y X Y X Y X 31
Y X Y X 32
Tampilkan video di sini https://www.youtube.com/watch?v=5dGcxBkB-tM 33
وََترَى الجِبَالَْ َتحسَبُهَاْ جَامَِدْة وهِيََْتمُُْرّ َمْر السحَاْبِصُنْعَ اّلٰلِْ الذِٓيْٰ اَتقَنَْ كُلْ شَيءْ اِنْه خَبِيرْ ۚبِمَاْ َتفعَُلونَْ ’A A 34
Pergeseran sesuai arah sumbu Pergeseran sesuai arah sumbu X, yaitu ke kiri jika negatif X, yaitu ke kanan jika positif 35
Pergeseran sesuai arah sumbu Y, yaitu ke atas jika positif Pergeseran sesuai arah sumbu Y, yaitu ke bawah jika negatif https://qrgo.page.link/UQyYR 36
(4,0) ( 0 , -6 ) ( -8 , 5 ) (a,b) (-15, -12) 37
(-12, 8) y = -18 (24, -15) (30, -32) 38
(-9, -4) y = -4 (-9, -4) y = -4 (-9, -4) y = -4 Kini saatnya kalian mengerjakan kuis…. 39
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Tampilkan video https://www.youtube.com/watch?v=3wHbFtoyDi4 اِْن المُصدِقِيْنَ وَالمُصدِٰقَتِْوَاَقرَضُوا اّلٰلَْقَرضا حَسَنا ُّي ٰضَعَفَُْلهُْم وََلهُمْ اَجرْ كَرِيمْ 46
8 satuan 4 satuan 4 satuan 2 satuan 47
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