LOW is at: L (-5,-2), O (-2,-4), W (-4,-

L'O'W' is at L' (-5,10), O' (-2,8), W (-4,6)

ΔLOW→ΔL"O"W" looks like a translation. What two moves could replace the one translation?

(1 point)
Responses

a reflection across parallel lines
a reflection across parallel lines

a reflection across intersecting lines
a reflection across intersecting lines

a counterclockwise rotation of 180 degrees
a counterclockwise rotation of 180 degrees

a reflection across perpendicular lines

1 answer

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:

  1. A reflection across parallel lines.
  2. A reflection across intersecting lines.
  3. A counterclockwise rotation of 180 degrees.
  4. 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.