TRANSFORMASI

4. Tentukan bayangan-bayangan dari

   1. garis $x+2y+3=0$ oleh translasi $\left(\begin{array}{c}1\\ 1\end{array}\right)$

   2. kurva $y=x^2$ oleh translasi $\left(\begin{array}{c}2\\ -1\end{array}\right)$

   3. kurva $x^2+y^2-2x-10y-10=0$ oleh translasi $\left(\begin{array}{c}-2\\ 3\end{array}\right)$

Gunakan : $y=f\left(x\right)\stackrel{ \left(\begin{array}{c}a\\ b\end{array}\right) }{\to }y-b=f\left(x-a\right)$

1. Garis $x+2y+3=0$ oleh translasi $\left(\begin{array}{c}1\\ 1\end{array}\right)$

   $x+2y+3=0\stackrel{ \left(\begin{array}{c}1\\ 1\end{array}\right) }{\to }\left(x-1\right)+2\left(y-1\right)+3=0$

   Bayangannya : $x+2y=0$

2. Kurva $y=x^2$ oleh translasi $\left(\begin{array}{c}2\\ -1\end{array}\right)$

   $y=x^2\stackrel{ \left(\begin{array}{c}2\\ -1\end{array}\right) }{\to }\left(y+1\right)={\left(x-2\right)}^2$

   $y+1=x^2-4x+4$

   Bayangannya : $y=x^2-4x+3$

3. Kurva $x^2+y^2-2x-10y-10=0$ oleh translasi $\left(\begin{array}{c}-2\\ 3\end{array}\right)$

   Lingkaran $x^2+y^2-2x-10y-10=0$ $\leftrightarrow$ ${\left(x-1\right)}^2+{\left(y-5\right)}^2=36$

   ${\left(x-1\right)}^2+{\left(y-5\right)}^2=36\mathrm{ }\stackrel{ \left(\begin{array}{c}-2\\ 3\end{array}\right) }{\to }{\left(\underbrace{x+2}-1\right)}^2+{\left(\underbrace{y-3}-5\right)}^2=36\mathrm{ }$

   ${\left(x+1\right)}^2+{\left(y-8\right)}^2=36$

   Bayangannya : ${\left(x+1\right)}^2+{\left(y-8\right)}^2=36$