KOMPOSISI TRANSFORMASI Transformasi \left[\begin{array}{ccc}2&1\\-1&-3\end{array}\right] [/tex] ter.... Question from @rizalvp

September 2018 1 102 Report

KOMPOSISI TRANSFORMASI

Transformasi $\left[\begin{array}{ccc}a&a+1\\1&-2\end{array}\right] yang dilanjutkan oleh transformasi$ \left[\begin{array}{ccc}2&1\\-1&-3\end{array}\right] [/tex] terhadap titik A(2,3) dan B(4,1) menghasilkan bayangan A'(22,-1) dan B'(24,-17).

a. Tentukan nilai a !
b. Tentukan bayangan titik P(8,11) oleh transformasi tersebut !
c. Tentukan koordinat titik Q jika bayangan titik Q adalah Q'(70,35)

madewas $\left[\begin{array}{ccc}22\\-1\\\end{array}\right]$ = $\left[\begin{array}{ccc}2&1\\-1&-3\\\end{array}\right]$ $\left[\begin{array}{ccc}a&a+1\\1&-2\\\end{array}\right]$ $\left[\begin{array}{ccc}2\\3\\\end{array}\right]$
$\left[\begin{array}{ccc}22\\-1\\\end{array}\right]$ = $\left[\begin{array}{ccc}2a+1&2a+2-2\\-a-3&-a-1+6\\\end{array}\right]$ $\left[\begin{array}{ccc}2\\3\\\end{array}\right]$
$\left[\begin{array}{ccc}22\\-1\\\end{array}\right]$ = $\left[\begin{array}{ccc}4a+2+6a\\-2a-6-3a+15\\\end{array}\right]$
22 = 4a+2+6a
22 = 10a+2
-2+22 = 10a
20 = 10a
a = 2

$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right]$ = $\left[\begin{array}{ccc}2&1\\-1&-3\\\end{array}\right]$ $\left[\begin{array}{ccc}2&3\\1&-2\\\end{array}\right]$ $\left[\begin{array}{ccc}8\\11\\\end{array}\right]$
$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right]$ = $\left[\begin{array}{ccc}4+1&6-2\\-2-3&-3+6\\\end{array}\right]$ $\left[\begin{array}{ccc}8\\11\\\end{array}\right]$
$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right]$ = $\left[\begin{array}{ccc}5&4\\-5&3\\\end{array}\right]$ $\left[\begin{array}{ccc}8\\11\\\end{array}\right]$
$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right]$ = $\left[\begin{array}{ccc}84\\-7\\\end{array}\right]$
bayangan titik P adalah P'(84,-7)

$\left[\begin{array}{ccc}70\\35\\\end{array}\right]$ = $\left[\begin{array}{ccc}2&1\\-1&-3\\\end{array}\right]$ $\left[\begin{array}{ccc}2&3\\1&-2\\\end{array}\right]$ $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$
$\left[\begin{array}{ccc}70\\35\\\end{array}\right]$ = $\left[\begin{array}{ccc}4+1&6-2\\-2-3&-3+6\\\end{array}\right]$ $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$
$\left[\begin{array}{ccc}70\\35\\\end{array}\right]$ = $\left[\begin{array}{ccc}5&4\\-5&3\\\end{array}\right]$ $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$
70 = 5x+4y
35 = -5x+3y
------------------- (+)
105 = 7y
y = 105/7 = 15

5x+4(15) = 70
5x = 70 - 60 = 10
x = 2
jadi koordinat titik Q(2,15)

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