\begin{tabular}{l} Determine the type of transformation represented by the following matrix. \ {$$ \left[\begin{array}{ll}9 & 0 \ 0 & 1\end{array} ight] $$} \ \begin{tabular}{|l|l|l}$$ \checkmark $$ Select \ Horizontal expansion \ Horizontal contraction \ Vertical contraction \ Vertical expansion \end{tabular} \ \hline\end{tabular}

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\begin{tabular}{l} Determine the type of transformation represented by the following matrix. \ {$$ \left[\begin{array}{ll}9 & 0 \ 0 & 1\end{array}ight] $$} \ \begin{tabular}{|l|l|l}$$ \checkmark $$ Select \ Horizontal expansion \ Horizontal contraction \ Vertical contraction \ Vertical expansion \end{tabular} \ \hline\end{tabular}

UpStudy AI · Accepted Answer

1. The given matrix is 
   $$
   \begin{pmatrix}
   9 & 0 \
   0 & 1
   \end{pmatrix}.
   $$

2. This matrix transforms a point $$(x, y)$$ in the plane as follows:
   $$
   \begin{pmatrix}
   9 & 0 \
   0 & 1
   \end{pmatrix}
   \begin{pmatrix}
   x \
   y
   \end{pmatrix}
   =
   \begin{pmatrix}
   9x \
   y
   \end{pmatrix}.
   $$

3. The $$x$$-coordinate is multiplied by $$9$$, while the $$y$$-coordinate remains unchanged.

4. Since the horizontal component is scaled by a factor greater than $$1$$ (specifically, $$9$$), the transformation represents a **horizontal expansion**.

5. Therefore, the correct selection is:
   - Horizontal expansion.
The transformation is a horizontal expansion.

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