Question
Determine whether the statement is true or false. The lines \( x=-4 \) and \( x=4 \) are perpendicular.
Ask by Ryan Ruiz. in the United States
Feb 20,2025
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Answer
The lines \( x = -4 \) and \( x = 4 \) are not perpendicular.
Solution
To determine whether the lines \( x = -4 \) and \( x = 4 \) are perpendicular, we need to analyze the nature of these lines.
1. **Understanding the lines**:
- The line \( x = -4 \) is a vertical line that passes through the point (-4, y) for all values of y.
- The line \( x = 4 \) is also a vertical line that passes through the point (4, y) for all values of y.
2. **Perpendicular lines**:
- Two lines are considered perpendicular if the product of their slopes is -1.
- Vertical lines have an undefined slope, and they do not intersect at a right angle with each other.
Since both lines are vertical, they are parallel to each other, not perpendicular.
Therefore, the statement is **false**.
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Simplify this solution Extra Insights
The statement is false. The lines \( x = -4 \) and \( x = 4 \) are both vertical lines. Vertical lines are parallel to each other and do not intersect, meaning they cannot be perpendicular. In fact, for two lines to be perpendicular, they need to intersect at a right angle, which cannot happen with vertical lines. In summary, while vertical lines maintain a distinct relationship, they simply run parallel to each other, making the claim about their perpendicularity incorrect.
