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The image contains several geometry and algebra problems written in Persian. Here are the translations and descriptions for some of the problems:

1. **(a) For \( k = 1 \): Draw the mentioned line. In which region does its graph lie?**
   
2. **(b) What is the width of the area \( k = y \)?**

3. **(c) For which \( x \) value is the width of the area \( \frac{1}{x} \)?**

4. **(7) Given the vertices of the quadrilateral \( A(2,3) \), \( B(k,1) \), \( C(-1,0) \): Calculate the slope of diagonal \( AC \). Is there a value of \( k \) such that \( AB \) and \( BC \) are perpendicular?**

5. **(Two vertices of line segment \( AB \) are \( A(2,3) \) and \( B(-1,2) \)):**
    - (a) Find the equation of the line that passes through point \( A \) and is perpendicular to \( AB \).
    - (b) Find the equation of the line that is parallel to \( AB \).

These are the types of problems covered in the image. Please let me know if you would like to solve a specific problem or if you need detailed solutions and explanations.

**5 Relative Questions:**

1. How do you determine the slope of a line passing through two points?
2. What is the general formula for the equation of a line perpendicular to a given line?
3. How do you find the width of a geometric area on a coordinate plane?
4. What conditions must two lines meet to be perpendicular?
5. How can you determine if a quadrilateral is a specific type (like a rectangle or parallelogram) based on its vertices?

**Tip:** To check perpendicularity between two lines, their slopes should be negative reciprocals of each other.

Multiple geometry and algebra problems involving line equations, slopes, and geometric areas on a coordinate plane.

Explore multiple coordinate geometry problems involving slope calculations, line equations, perpendicularity, and parallelism. These problems test key concepts such as the slope theorem and how to determine if lines are perpendicular or parallel. Suitable for students in Grades 9-11.

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