Tentukan bayangan titik-titik berikut setelah dirotasikan terhadap titik O(0, 0) sebesar sudut yang diberikan. (Transformasi geometri) a. (4, 2) dan theta = 60 deg b. (-5,-5) dan theta = 135 deg c. (1, 1) dan theta = 315 deg d. (-3, 6) dan theta = - 240 deg

<p><br>Rumus Umum Rotasi Pusat O(0,0)<br>x' = x cos theta - y sin theta<br>y' = x sin theta + y cos theta<br>A. Titik (4, 2) dan theta = 60 derajat<br>* Nilai Trigonometri: cos 60 = 1/2, sin 60 = (akar 3)/2<br>* Perhitungan:<br>&nbsp; x' = 4(1/2) - 2((akar 3)/2) = 2 - akar 3<br>&nbsp; y' = 4((akar 3)/2) + 2(1/2) = 2(akar 3) + 1<br>* Hasil: (2 - akar 3, 1 + 2 akar 3)<br>B. Titik (-5, -5) dan theta = 135 derajat<br>* Nilai Trigonometri: cos 135 = -1/2 akar 2, sin 135 = 1/2 akar 2<br>* Perhitungan:<br>&nbsp; x' = (-5)(-1/2 akar 2) - (-5)(1/2 akar 2) = 5/2 akar 2 + 5/2 akar 2 = 5 akar 2<br>&nbsp; y' = (-5)(1/2 akar 2) + (-5)(-1/2 akar 2) = -5/2 akar 2 + 5/2 akar 2 = 0<br>* Hasil: (5 akar 2, 0)<br>C. Titik (1, 1) dan theta = 315 derajat<br>* Nilai Trigonometri: cos 315 = 1/2 akar 2, sin 315 = -1/2 akar 2<br>* Perhitungan:<br>&nbsp; x' = 1(1/2 akar 2) - 1(-1/2 akar 2) = 1/2 akar 2 + 1/2 akar 2 = akar 2<br>&nbsp; y' = 1(-1/2 akar 2) + 1(1/2 akar 2) = -1/2 akar 2 + 1/2 akar 2 = 0<br>* Hasil: (akar 2, 0)<br>D. Titik (-3, 6) dan theta = -240 derajat (ekuivalen 120 derajat)<br>* Nilai Trigonometri: cos 120 = -1/2, sin 120 = (akar 3)/2<br>* Perhitungan:<br>&nbsp; x' = (-3)(-1/2) - 6((akar 3)/2) = 3/2 - 3 akar 3<br>&nbsp; y' = (-3)((akar 3)/2) + 6(-1/2) = -3/2 akar 3 - 3<br>* Hasil: (3/2 - 3 akar 3, -3 - 3/2 akar 3)</p>