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To determine the number of lines that are perpendicular to line \( w \), we need to observe the relationship between line \( w \) and the other lines \( x \), \( y \), and \( z \).

- Two lines are perpendicular if they intersect at a right angle (90 degrees).
- Looking at the diagram:
  - Line \( w \) is vertical.
  - Line \( y \) is horizontal, meaning it is perpendicular to \( w \) because vertical and horizontal lines form 90-degree angles.
  - Lines \( x \) and \( z \) are diagonal and do not appear to form right angles with line \( w \).

Therefore, the only line that is perpendicular to line \( w \) is line \( y \).

**Answer: B. 1**

Do you want more details or have any questions?

Here are five related questions to expand on this:
1. What conditions must two lines satisfy to be perpendicular?
2. How can we determine if diagonal lines are perpendicular to a vertical line?
3. How would the answer change if line \( z \) were vertical?
4. Can two non-parallel diagonal lines be perpendicular to each other?
5. How do we find the angle between two intersecting diagonal lines?

**Tip:** Always remember that vertical and horizontal lines are perpendicular to each other by definition.

What is the total number of lines that are perpendicular to line w?

In this geometry problem, students are asked to find how many lines are perpendicular to a given line in a diagram with four intersecting lines. This problem involves understanding perpendicularity and basic geometric principles.

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