Write an equation of the line through the pointers (a) parallel to the given line (b)perpendicular to the given line Point(2.5) linex x=0

Let's address the problem step by step. You need to find the equations of lines that pass through the point \( (2, 5) \) and are either:

1. Parallel to the given line.
2. Perpendicular to the given line.

### Given Line
The given line is \( x = 0 \). This is a vertical line passing through all points where the x-coordinate is 0.

### (a) Parallel Line

- A line parallel to \( x = 0 \) must also be a vertical line.
- Since the line needs to pass through the point \( (2, 5) \), the equation of the parallel line will be \( x = 2 \).

### (b) Perpendicular Line

- A line perpendicular to a vertical line is a horizontal line.
- A horizontal line has an equation of the form \( y = \text{constant} \).
- Since the line needs to pass through the point \( (2, 5) \), the equation of the perpendicular line will be \( y = 5 \).

### Final Answer

- **Equation of the line parallel to \( x = 0 \):** \( x = 2 \)
- **Equation of the line perpendicular to \( x = 0 \):** \( y = 5 \)

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What is the general form of the equation of a vertical line?
2. How do you determine if two lines are parallel?
3. How do you find the slope of a line?
4. What is the equation of a line passing through two given points?
5. How do you determine if two lines are perpendicular?

**Tip:** Remember, vertical lines have an undefined slope, while horizontal lines have a slope of zero.

Learn how to find equations of lines parallel and perpendicular to the line x = 0 with a step-by-step solution. Understand the concepts of parallel and perpendicular lines in geometry. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation