To determine the value of \( k \) based on the transformation of the original ordered pair \((8, 2)\) to the transformed ordered pair \((2, 2)\), we can identify how the transformation affects the \( x \)-coordinate.
- The original \( x \)-coordinate is \( 8 \).
- The transformed \( x \)-coordinate is \( 2 \).
If this transformation is likely a horizontal scaling by a factor of \( k \), we have the formula:
\[ x' = \frac{x}{k} \]
where \( x' \) is the transformed \( x \)-coordinate.
Setting this up with the given coordinates:
\[ 2 = \frac{8}{k} \]
Now, we can solve for \( k \):
\[ 2k = 8 \]
\[ k = \frac{8}{2} = 4 \]
Thus, the value of \( k \) is \( 4 \).