To determine the value of \( k \) and the type of transformation, we need to compare the \( x \)-coordinates of the original point and the transformed point.
The original ordered pair is \( (4, 9) \) and the transformed ordered pair is \( (2, 9) \). The \( y \)-coordinates remain the same, indicating that there is no vertical transformation, only a horizontal transformation.
The transformation affects the \( x \)-coordinate from \( 4 \) to \( 2 \). The dilation factor \( k \) can be calculated using the formula for horizontal dilation:
\[ \text{New } x = \frac{\text{Old } x}{k} \]
Substituting the values, we have:
\[ 2 = \frac{4}{k} \]
To solve for \( k \):
- Multiply both sides by \( k \):
\[ 2k = 4 \]
- Divide both sides by \( 2 \):
\[ k = 2 \]
Since the value of \( k \) is 2, this indicates a horizontal compression. A horizontal compression occurs when \( k > 1 \).
Thus, the correct identification from the options provided is:
k = 2; compression
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