LEMBAR AKTIVITAS SISWA – HUBUNGAN ANTAR GARIS Nama Siswa : _____ Kelas : ... Gradien garis yang sejajar dengan sumbu y, maka gradiennya
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LEMBAR AKTIVITAS SISWA – TRANSFORMASI GEOMETRI Contoh 1: Nama Siswa
: ___________________
Kelas
: ___________________ Jawab:
Kompetensi Dasar (Kurikulum 2013): 3.4 Menerapkan konsep dan aturan komposisi transformasi geometri koordinat dalam menyelesaikan matematika dan masalah kontekstual. 4.4 Memecahkan masalah dengan menggunakan konsep dan aturan komposisi beberapa transformasi geometri koordinat. A. KOMPOSISI TRANSFORMASI GEOMETRI
Contoh 2:
Jawab:
Latihan 1 1.
1. Komposisi Translasi JIka translasi pertama yang dinyatakan dengan T1 dilanjutkan Jawab:
dengan transformasi kedua yang dinyatakan dengan T2 maka komposisi translasinya dapat ditulis dengan: T2 o T1
2.
Jawab: Pada komposisi translasi berlaku: (sifat komutatif)
1
King’s Learning Be Smart Without Limits
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3. 6.
Jawab:
Jawab:
4.
Jawab: 2. Komposisi Refleksi Dua refleksi atau lebih yang dilakukan secara berurutan disebut komposisi refleksi. Penulisan refleksi oleh M1 dilanjutkan oleh matriks M2 adalah M2 o M1 (dibaca: M2 noktah M1) ditentukan oleh: M2 o M1 = M2 . M1 (perkalian matriks) Jika titik (x,y) direfleksikan dengan M1 menghasilkan (x’,y’) dan dilanjutkan dengan refleksi M2 menghasilkan (x’’,y’’) maka dapat dituliskan dengan:
5.
Jawab:
2
Bentuk-bentuk matriks pada transformasi refleksi:
King’s Learning Be Smart Without Limits
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Contoh 3:
Komposisi Refleksi Khusus Jika titik A(x,y) direleksikan terhadap garis x = h 1 dan dilanjutkan terhadap garis x = h2, diperoleh bayangan:
Jawab:
A” (2(h2-h1) + x , y) Persamaan Matriks:
Secara Geometri Analitik:
Contoh 4: Tentukan bayangan 2x + 3y + 1 = 0 jika direfleksikan ke garis y = -x dan kemudian terhadap sumbu y. Jawab:
Jika titik A(x,y) direleksikan terhadap garis y = k1 dan dilanjutkan terhadap garis y = k2, diperoleh bayangan: A” (x , 2(k2-k1)+y) Persamaan Matriks:
