To understand how the triangle \( \Delta LOW \) transforms to \( \Delta L'O'W' \), we can analyze the changes in the coordinates of each vertex.
The initial points are:
- \( L (-5, -2) \)
- \( O (-2, -4) \)
- \( W (-4, ?) \) (the y-coordinate of W is missing)
The transformed points are:
- \( L' (-5, 10) \)
- \( O' (-2, 8) \)
- \( W' (-4, 6) \)
Looking at the changes in the y-coordinates for points L and O:
- From \( L (-5, -2) \) to \( L' (-5, 10) \), the y-coordinate changed from -2 to 10 (a rise of 12 units).
- From \( O (-2, -4) \) to \( O' (-2, 8) \), the y-coordinate changed from -4 to 8 (a rise of 12 units).
This consistent rise suggests that there may be a transformation involved.
The options given for transformations are:
- A reflection across parallel lines.
- A reflection across intersecting lines.
- A counterclockwise rotation of 180 degrees.
- A reflection across perpendicular lines.
In this case, the movement could be a reflection across two parallel lines with a translation as the final transformation to account for the consistent vertical shift in y-coordinates.
Thus, the answer is: a reflection across parallel lines.