To determine the value of \( k \) in the given transformation from the original ordered pair (8, 2) to the transformed ordered pair (2, 2), we can examine the effect this transformation has on each component of the ordered pair, specifically the x-coordinate.
The transformation can be expressed in the form:
\[ (x, y) \rightarrow (kx, y) \]
Here, \( k \) represents the scaling factor applied to the x-coordinate.
Given:
- Original point: \( (8, 2) \)
- Transformed point: \( (2, 2) \)
From the original point \( (8, 2) \) to the transformed point \( (2, 2) \):
- The y-coordinate remains the same (2), indicating no transformation in the y-direction.
- The x-coordinate changes from 8 to 2.
We can set up the equation:
\[ kx = 2 \]
Substituting the original x-coordinate (8) into the equation:
\[ k \cdot 8 = 2 \]
To solve for \( k \), divide both sides by 8:
\[ k = \frac{2}{8} = \frac{1}{4} \]
Thus, the value of \( k \) is \( \frac{1}{4} \).