To determine the value of \( k \) and whether the transformation is a compression or a stretch, we can look at the transformation of the x-coordinates in the ordered pairs.
- The original ordered pair is \( (8, 21) \)
- The transformed ordered pair is \( (2, 21) \)
To identify the value of \( k \) in terms of a horizontal transformation, we can compare the x-coordinates:
The transformation from 8 to 2 can be described by the equation: \[ x' = k \cdot x \] Plugging in the values: \[ 2 = k \cdot 8 \]
Solving for \( k \): \[ k = \frac{2}{8} = \frac{1}{4} \]
Since \( k < 1 \) (specifically \( k = \frac{1}{4} \)), this indicates a compression.
Thus, the correct identification is:
- The value of \( k \) is \( \frac{1}{4} \).
- This represents a horizontal compression.
So to answer:
- \( k = \frac{1}{4} \)
- It is a compression.