The image shows a question about identifying and working with parallel lines. Based on the lines depicted in the image:

a. Which line is parallel to line $t$?

• Answer: Line $k$ is parallel to line $t$. Both lines run in the same direction and do not intersect.

b. To obtain line $k$ from line $t$:

• Answer: You would translate line $t$ upward to align with line $k$. Translation means shifting the line without rotating or flipping it.

c. To obtain line $p$ from line $t$:

• Answer: To obtain line $p$, you would rotate line $t$ around a point. Line $p$ has a different orientation compared to line $t$, so rotation is the best method to match its position.

Would you like more details or clarifications on any of these points?

Here are 5 related questions you could explore:

1. How do you determine if two lines are parallel based on their slopes?
2. What are the characteristics of parallel lines in different geometries?
3. What transformations preserve the parallelism between two lines?
4. Can lines that never intersect but are not in the same plane be considered parallel (e.g., skew lines)?
5. What is the effect of reflecting a line on its slope and orientation?

Tip: When working with transformations, remember that translations and reflections preserve the distance between points on the line but affect the position and orientation differently!