Question

each column of the matrix $a = \

$$\begin{bmatrix} 1 & 6 & 6 & 1 \\\\ 1 & 1 & 5 & 5 \\end{bmatrix}$$

$ represents a vertex of a rectangle on the coordinate plane. if fan scales the rectangle by finding $4a$, what are the vertices of the scaled rectangle?\
\bigcirc \\ (4, 4), (24, 4), (24, 20), (4, 20)\
\bigcirc \\ (5, 5), (10, 5), (10, 9), (5, 9)\
\bigcirc \\ (4, 4), (6, 1), (6, 5), (1, 5)\
\bigcirc \\ (5, 5), (6, 1), (6, 5), (4, 20)

Explanation:

Step1: Multiply matrix \(A\) by scalar \(4\)

Given \(A=

$$\begin{bmatrix}1&6&6&1\\1&1&5&5\end{bmatrix}$$

\), then \(4A = 4\times

$$\begin{bmatrix}1&6&6&1\\1&1&5&5\end{bmatrix}$$

=

$$\begin{bmatrix}4\times1&4\times6&4\times6&4\times1\\4\times1&4\times1&4\times5&4\times5\end{bmatrix}$$

\)

Step2: Calculate each element

\(4\times1 = 4\), \(4\times6=24\), \(4\times5 = 20\). So \(4A=

$$\begin{bmatrix}4&24&24&4\\4&4&20&20\end{bmatrix}$$

\)

Step3: Write vertices

The columns of \(4A\) give the vertices \((4,4)\), \((24,4)\), \((24,20)\), \((4,20)\)

Answer:

\((4,4),(24,4),(24,20),(4,20)\) (First option)