uplakanimkk

2022-07-03

Using matrix methods, how to find the image of the point (1,-2) for the transformations?
1) a dilation of factor 3 from the x-axis
2) reflection in the x-axis

Expert

MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document 1) multiply the coordinates by the scale factor
$⇒\left(\begin{array}{c}x\prime \\ y\prime \end{array}\right)=3\left(\begin{array}{c}1\\ -2\end{array}\right)=\left(\begin{array}{c}3\\ -6\end{array}\right)$
$⇒\left(1,-2\right)\to \left(3,-6\right)$
2) multiply by the associated reflection matrix
for reflection in the x-axis
$•x\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$
$⇒\left(\begin{array}{c}x\prime \\ y\prime \end{array}\right)=\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)$
$=\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)\left(\begin{array}{c}1\\ -2\end{array}\right)=\left(\begin{array}{c}1\\ 2\end{array}\right)$
$⇒\left(1,-2\right)\to \left(1,2\right)$

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