Question

Triangle LOW -> Triangle L" O" W" looks like a translation. What two moves could replace the one translation?
Triangle LOW
Point L: (-5, -2)
Point O: (-2, -4)
Point W: (-4, -6)

Triangle L"O"W"
Point L": (-5, 10)
Point O": (-2, 8)
Point W": (-4, 6)

A. a reflection across intersecting lines
B. a counterclockwise rotation of 180 degrees
C. a reflection across perpendicular lines
D. a reflection across parallel lines

Answer 1

To determine which two moves could replace the translation from triangle LOW to triangle L"O"W", we first need to analyze the transformation.

Points of Triangle LOW:
- L: (-5, -2)
- O: (-2, -4)
- W: (-4, -6)

Points of Triangle L"O"W":
- L": (-5, 10)
- O": (-2, 8)
- W": (-4, 6)

### Step 1: Identify the translation vector
To get from each point of triangle LOW to triangle L"O"W", we will look at the changes in the y-coordinates:

- L: from -2 to 10 (increase of 12)
- O: from -4 to 8 (increase of 12)
- W: from -6 to 6 (increase of 12)

The translation moves each y-coordinate up by 12 units, staying in the same x-coordinates.

### Step 2: Explore possible moves
Now let's denote the possible choices:

- A. a reflection across intersecting lines
- B. a counterclockwise rotation of 180 degrees
- C. a reflection across perpendicular lines
- D. a reflection across parallel lines

### Analysis of Two Moves
Since the translation is a consistent vertical shift, we need a combination of transformations that can jointly produce the outcome of translating all points upward in a consistent manner.

- **A Reflection across intersecting lines** generally changes both x and y coordinates in a non-linear way, making this improbable.

- **B Counterclockwise rotation of 180 degrees** will rotate each point around the origin, which will change both coordinates, thus this option does not seem to work.

- **C Reflection across perpendicular lines** could involve sequential transformations, but aligning them perfectly to match the upward shift in y-coordinates is complex and potentially does not yield the same outcome.

- **D Reflection across parallel lines** followed by another transformation could align the points vertically without affecting their horizontal alignment.

### Possible Conclusion
Based on the transformation characteristics and the requirement to achieve the same effect through two moves it would most feasibly be (D) since reflecting across a parallel line could catch the upward shift and then potentially another transformation could align it correctly.

Thus, the correct choice would be: **D. a reflection across parallel lines.**

### Final Assertion
To verify further, we can also consider practical attempts or geometric tools, but for theoretical reasoning, the reasoning points toward option D as the most valid route to match the output of the translation described.