Soal Transformasi Geometri Kelas 9 Extra Quality Review

The Treasure of Mirrored Island In a quiet classroom in Yogyakarta, nine students of Class 9B were staring at a whiteboard filled with coordinate grids. Their teacher, Ibu Dewi, had just written: “ULANGAN HARIAN: TRANSLASI, REFLEKSI, ROTASI, DILATASI.” Among them sat Bimo, who loved history but found math as confusing as a tangled thread. He looked at the sample problem:

Titik A(3,4) ditranslasikan oleh T(2,-1). Tentukan koordinat A’.

“Just move it,” he mumbled. “Two steps right, one step down. A’(5,3). That’s easy. But why does this matter in real life?” Ibu Dewi must have read his mind. She smiled and said, “Class, your real test isn’t on paper today. It’s in the school’s old library. Someone has hidden the key to the ‘Lumbini Chest’—a box full of ancient Javanese relics. To find it, you must solve four transformation problems. Work as a team.” The class buzzed with excitement. Bimo’s heart raced. A treasure hunt? Clue 1: The Translation (Pergeseran) Inside a dusty encyclopedia, they found a note:

“Start at the statue of Ganesha (0,0). Geser (shift) by T(4,3). Where do you stand?” Soal Transformasi Geometri Kelas 9

“That’s easy,” said Sari, the math whiz. “(0+4, 0+3) = (4,3). The old well!” They ran to the well. Taped underneath the bucket was a small mirror. Clue 2: The Reflection (Pencerminan) On the mirror’s back, another clue:

“Cerminkan titik (7,2) terhadap sumbu Y (x=0).”

“Reflection over the Y-axis changes the sign of x,” said Bimo, suddenly confident. “(7,2) becomes (-7,2). That’s the headmaster’s office!” Sure enough, on the office door hung a compass. Clue 3: The Rotation (Perputaran) Inside the compass case was a riddle: The Treasure of Mirrored Island In a quiet

“Putar titik (-3,1) sejauh 90° berlawanan arah jarum jam dengan pusat (0,0).”

The team gathered. “Rotation 90° counterclockwise,” explained Sari, “changes (x,y) to (-y,x). So (-3,1) becomes (-1,-3).” Bimo checked the school map. “That’s not a room. That’s the (-1,-3) coordinate… behind the banyan tree, near the old flagpole.” They dug a little and found a locked chest. The lock had four dials. Clue 4: The Dilation (Perbesaran) The final clue was carved on the chest:

“Titik kunci: (2,3) didilatasikan dengan pusat (0,0) dan faktor skala 3. Jumlah x + y = kode pembuka.” Tentukan koordinat A’

“Dilation multiplies,” said Bimo, calculating. “(2×3, 3×3) = (6,9). Then x + y = 6 + 9 = 15.” He turned the dials to 1-5. Click! Inside the chest were not gold or jewels, but old scrolls and a note: “Ilmu transformasi geometri adalah peta. Pahami peta ini, dan kau tak akan tersesat, baik dalam ujian maupun kehidupan.” (The knowledge of geometric transformations is a map. Understand this map, and you will never get lost, whether in an exam or in life.) That night, Bimo opened his math book. The problems—once foreign symbols—now looked like treasure clues. Sample problems from Bimo’s notebook:

Translation: Titik P(5,-2) ditranslasikan oleh T(-3,4). Bayangan P’ adalah? (Answer: (2,2)) Reflection: Bayangan titik Q(-4,6) jika dicerminkan terhadap garis y = x adalah? (Answer: (6,-4)) Rotation: Titik R(3,-5) dirotasi 180° dengan pusat O(0,0). Tentukan R’. (Answer: (-3,5)) Dilation: Titik S(4,6) didilatasi [O, ½]. Luas bayangan persegi panjang dengan titik tersebut menjadi… (Answer: ¼ luas awal)