To determine the value of \( k \) and whether the transformation is a compression or a stretch, we can analyze the given ordered pairs.
The original ordered pair is \( (2, 9) \) and the transformed ordered pair is \( (6, 9) \). From this, we can see that the y-coordinates remain the same (both are 9), while the x-coordinates change from 2 to 6.
This transformation affects the x-coordinate. We can conceptualize this transformation as changing \( x \) by a factor of \( k \):
\[ k = \frac{\text{New } x}{\text{Original } x} = \frac{6}{2} = 3 \]
Since the value of \( k \) is greater than 1, it indicates a stretch in the x-direction. In general, a stretch occurs when \( k > 1 \) and a compression occurs when \( k < 1 \).
Based on the options provided, the correct identification would be:
- \( k = 3 \)
- This is a stretch.
So the answer is Three stretch.