Question

yo yg bisa bantu nya jangan ngasalah
kalo ngasal gw repot ​

Answer 1

Jawaban:

1. refleksi

2. [tex]T= \begin{pmatrix}5\\3\end{pmatrix}[/tex]

3. (-3, 5)

4. titik O (0,0)

5. x=2y + 7

Penjelasan dengan langkah-langkah:

Transformasi Geometri

Translasi (pergeseran)

[tex] \boxed{ \begin{array}{c}A(x,y) \xrightarrow{T = \binom{a}{b}}A'(x',y')\\\\ \begin{pmatrix}x'\\y'\end{pmatrix}= \begin{pmatrix}x\\y\end{pmatrix}+ \begin{pmatrix}a\\b\end{pmatrix} \end{array}}[/tex]

Refleksi (pencerminan)

[tex] \small \boxed{\begin{array}{l | l} rumus & matriks \\ \hline A(x,y) \xrightarrow{\: \:M_{x}\: \:}A'(x,-y)& \begin{pmatrix}1&0\\0&-1\end{pmatrix}\\A(x,y) \xrightarrow{ \: \: M_{y} \: \: }A'(-x,y)& \begin{pmatrix}-1&0\\0&-1\end{pmatrix}\\A(x,y) \xrightarrow{\: \:M_{y=x}\: \:}A'(y,x)& \begin{pmatrix}0&1\\1&0\end{pmatrix}\\A(x,y) \xrightarrow{\: \:M_{y=-x}\: \:}A'(-y,-x)& \begin{pmatrix}0&-1\\-1&0\end{pmatrix}\\A(x,y) \xrightarrow{\: \:M_{O}\: \:}A'( - x, - y)& \begin{pmatrix}-1&0 \\ 0&-1\end{pmatrix}\\A(-x,-y) \xrightarrow{\: \:M_{x=h}\: \:}A'(2h-x,y)& \begin{pmatrix}-1&0\\0&1\end{pmatrix} \begin{pmatrix}x\\y\end{pmatrix}+ \begin{pmatrix}2h\\0\end{pmatrix}\\A(x,y) \xrightarrow{\: \:M_{y=h}\: \:}A'(x,2h-y) &\begin{pmatrix}1&0\\0&-1\end{pmatrix} \begin{pmatrix}x\\y\end{pmatrix}+ \begin{pmatrix}0\\2h\end{pmatrix}\end{array}}[/tex]

[tex]_____________________[/tex]

penyelesaian

1. refleksi

[tex]________[/tex]

2.

A'=A+T

[tex]\begin{pmatrix}2\\-1\end{pmatrix} =\begin{pmatrix}-3\\4\end{pmatrix} +T [/tex]

[tex]T= \begin{pmatrix}2\\-1\end{pmatrix} -\begin{pmatrix}-3\\-4\end{pmatrix} [/tex]

[tex]T= \begin{pmatrix}5\\3\end{pmatrix} [/tex]

[tex]________[/tex]

3.

[tex]A(x,y) \xrightarrow{ \: \: M_{y} \: \: }A'(-x,y) \\ A(3,5) \xrightarrow{ \: \: M_{y} \: \: }A'(-3,5)[/tex]

[tex]________[/tex]

4.

[tex]R( - 2,7) \xrightarrow{ \: \: M_{ ?} \: \: }R'(2, - 7) \\ \sf \: didapatkan : x = - x \: \: dan \: \: y = - y \\ A(x,y) \xrightarrow{ \: \: M_{O} \: \: }A'( - x, - y)[/tex]

maka sumbu refleksi nya adalah titik O (0, 0)

[tex]________[/tex]

5. y=2x+7 dicerminkan terhadap garis y=x

[tex]\begin{pmatrix}x'\\y'\end{pmatrix}= \begin{pmatrix}0&1\\1&0\end{pmatrix} \begin{pmatrix}x\\y\end{pmatrix}[/tex]

[tex]\begin{pmatrix}x'\\y'\end{pmatrix}= \begin{pmatrix}y\\x\end{pmatrix}[/tex]

[tex]x '= y \rightarrow y = x' \\ y' = x \rightarrow x = y'[/tex]

y=2x+7

x' = 2(y') + 7

x = 2y + 7

atau bisa ditulis x - 2y - 7 = 0