Tolong di kerjakan ya..Persamaan bayangan garis x - 2y + 4 = 0 karena dirotasikan dengan pusat ( 0,0.... Question from @wenymeilinda

September 2018 1 62 Report

Tolong di kerjakan ya..
Persamaan bayangan garis x - 2y + 4 = 0 karena dirotasikan dengan pusat ( 0,0 ) sejauh 90 derajat dilanjutkan refleksi terhadap garis y = x adalah...
A. x + 2y + 4 = 0
B. x + 2y - 4 = 0
C 2x + y + 4 = 0
D. 2x - y - 4 = 0
E. 2x + y - 4 = 0.

Takamori37 Misalkan ambil dua titik untuk mempermudah yang melalui persamaan garis tersebut.
A(-4,0) dan B(0,2)
Dirotasikan pusat 90 derajat.
A' adalah:
$\left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}\cos 90&-\sin90\\ \sin 90&\cos 90\end{array}\right]\left[\begin{array}{cc}-4\\0\end{array}\right] \\\\ \left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}0&-1\\ 1&0\end{array}\right]\left[\begin{array}{cc}-4\\0\end{array}\right] \\\\ \left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}0\\-4\end{array}\right]$

B' adalah:
$\left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}\cos 90&-\sin90\\ \sin 90&\cos 90\end{array}\right]\left[\begin{array}{cc}0\\2\end{array}\right] \\\\ \left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}0&-1\\ 1&0\end{array}\right]\left[\begin{array}{cc}0\\2\end{array}\right] \\\\ \left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}-2\\0\end{array}\right]$

Direfleksikan dengan garis y = x
A'' adalah:
$\left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}0&1\\ 1&0\end{array}\right]\left[\begin{array}{cc}0\\-4\end{array}\right] \\\\ \left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}-4\\0\end{array}\right]$

B'' adalah:
$\left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}0&1\\ 1&0\end{array}\right]\left[\begin{array}{cc}-2\\0\end{array}\right] \\\\ \left[\begin{array}{cc}x'\\y'\end{array}\right]=\left[\begin{array}{cc}0\\-2\end{array}\right]$

Untuk persamaan garis yang melalui (a,0) dan (0,b) adalah:
bx + ay = ab
Maka,
-4x - 2y = 8
-2x - y = 4
2x + y + 4 = 0

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