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.