Tentukan Bayangan Titik A(2,3) dan B(1,4) pada rotasi -90 derajat dengan pusat rotasi P(-1,1)
jawabannya harus pake cara dan simple aja ya
makasih sebelumnya :)
jawabannya harus pake cara dan simple aja ya
makasih sebelumnya :)
ekamiaww
![matriks\ transformasinya\ adalah \\ \left[\begin{array}{ccc}cos (-90^o) &-sin (-90^o) \\sin (-90^o)&cos (-90^o)\end{array}\right] =\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \\ \left[\begin{array}{ccc}x'-a \\y'-b\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}x-a \\y-b\end{array}\right] \\ (x,y)\ =titik\ asal \\ (x',y')=titik\ bayangan \\ (a,b)=pusat\ rotasi \\ \\ bayangan\ titik\ A(2,3)\ dgn\ pusat\ rotasi\ P(-1,1)\ sejauh\ -90^o:](https://tex.z-dn.net/?f=matriks%5C+transformasinya%5C+adalah+%5C%5C+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dcos+%28-90%5Eo%29+%26-sin+%28-90%5Eo%29+%5C%5Csin+%28-90%5Eo%29%26cos+%28-90%5Eo%29%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0+%261+%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27-a++%5C%5Cy%27-b%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0+%261+%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-a+%5C%5Cy-b%5Cend%7Barray%7D%5Cright%5D+++%5C%5C+%28x%2Cy%29%5C+%3Dtitik%5C+asal+%5C%5C+%28x%27%2Cy%27%29%3Dtitik%5C+bayangan+%5C%5C+%28a%2Cb%29%3Dpusat%5C+rotasi+%5C%5C++%5C%5C+bayangan%5C+titik%5C+A%282%2C3%29%5C+dgn%5C+pusat%5C+rotasi%5C+P%28-1%2C1%29%5C+sejauh%5C+-90%5Eo%3A+ "matriks\ transformasinya\ adalah \\ \left[\begin{array}{ccc}cos (-90^o) &-sin (-90^o) \\sin (-90^o)&cos (-90^o)\end{array}\right] =\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \\ \left[\begin{array}{ccc}x'-a \\y'-b\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}x-a \\y-b\end{array}\right] \\ (x,y)\ =titik\ asal \\ (x',y')=titik\ bayangan \\ (a,b)=pusat\ rotasi \\ \\ bayangan\ titik\ A(2,3)\ dgn\ pusat\ rotasi\ P(-1,1)\ sejauh\ -90^o:")
![\left[\begin{array}{ccc}x'-(-1)\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}2-(-1) \\3-1\end{array}\right]\\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}3 \\2\end{array}\right] \\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]= \left[\begin{array}{ccc}2 \\-3\end{array}\right]\\ x'+1=2\\~~~~~~x'=2-1\\~~~~~~ x'=1\\ y'-1=-3\\ ~~~~~~y'=-3+1 \\ ~~~~~~y'=-2](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27-%28-1%29%5C%5Cy%27-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0+%261+%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2-%28-1%29+%5C%5C3-1%5Cend%7Barray%7D%5Cright%5D%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27%2B1%5C%5Cy%27-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0+%261+%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3+%5C%5C2%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27%2B1%5C%5Cy%27-1%5Cend%7Barray%7D%5Cright%5D%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2+%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%5C%5C+x%27%2B1%3D2%5C%5C%7E%7E%7E%7E%7E%7Ex%27%3D2-1%5C%5C%7E%7E%7E%7E%7E%7E+x%27%3D1%5C%5C+y%27-1%3D-3%5C%5C+%7E%7E%7E%7E%7E%7Ey%27%3D-3%2B1+%5C%5C+%7E%7E%7E%7E%7E%7Ey%27%3D-2 "\left[\begin{array}{ccc}x'-(-1)\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}2-(-1) \\3-1\end{array}\right]\\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}3 \\2\end{array}\right] \\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]= \left[\begin{array}{ccc}2 \\-3\end{array}\right]\\ x'+1=2\\~~~~~~x'=2-1\\~~~~~~ x'=1\\ y'-1=-3\\ ~~~~~~y'=-3+1 \\ ~~~~~~y'=-2")
![\left[\begin{array}{ccc}x'-(-1)\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}1-(-1) \\4-1\end{array}\right]\\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}2 \\3\end{array}\right] \\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]= \left[\begin{array}{ccc}3 \\-2\end{array}\right]\\ x'+1=3\\~~~~~~x'=3-1\\~~~~~~ x'=2\\ y'-1=-2\\ ~~~~~~y'=-2+1 \\ ~~~~~~y'=-1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27-%28-1%29%5C%5Cy%27-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0+%261+%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1-%28-1%29+%5C%5C4-1%5Cend%7Barray%7D%5Cright%5D%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27%2B1%5C%5Cy%27-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0+%261+%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2+%5C%5C3%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%27%2B1%5C%5Cy%27-1%5Cend%7Barray%7D%5Cright%5D%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3+%5C%5C-2%5Cend%7Barray%7D%5Cright%5D%5C%5C+x%27%2B1%3D3%5C%5C%7E%7E%7E%7E%7E%7Ex%27%3D3-1%5C%5C%7E%7E%7E%7E%7E%7E+x%27%3D2%5C%5C+y%27-1%3D-2%5C%5C+%7E%7E%7E%7E%7E%7Ey%27%3D-2%2B1+%5C%5C+%7E%7E%7E%7E%7E%7Ey%27%3D-1 "\left[\begin{array}{ccc}x'-(-1)\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}1-(-1) \\4-1\end{array}\right]\\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]=\left[\begin{array}{ccc}0 &1 \\-1&0\end{array}\right] \left[\begin{array}{ccc}2 \\3\end{array}\right] \\ \left[\begin{array}{ccc}x'+1\\y'-1\end{array}\right]= \left[\begin{array}{ccc}3 \\-2\end{array}\right]\\ x'+1=3\\~~~~~~x'=3-1\\~~~~~~ x'=2\\ y'-1=-2\\ ~~~~~~y'=-2+1 \\ ~~~~~~y'=-1")
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