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The problem is written in Persian and translates as follows:

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8. The two endpoints of line segment AB are points \( A(3, 1) \) and \( B(-1, 2) \).

(a) Find the equation of the line that passes through point \( A \) and is perpendicular to line segment \( AB \).

(b) Find the equation of the line that starts from a point parallel to line segment \( AB \).

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Let's solve the problem step by step.

### Part (a): Finding the equation of a line perpendicular to line segment AB
1. First, we calculate the slope of line segment \( AB \).
   \[
   m_{AB} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{-1 - 3} = \frac{1}{-4} = -\frac{1}{4}
   \]
2. A line perpendicular to line segment \( AB \) will have a slope that is the negative reciprocal of \( m_{AB} \).
   \[
   m_{\perp} = 4
   \]
3. The equation of a line with slope \( 4 \) passing through point \( A(3, 1) \) can be written in point-slope form:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting the values:
   \[
   y -

The two endpoints of line segment AB are points A(3, 1) and B(-1, 2). Find the equation of the line perpendicular to AB through point A and the equation of the line parallel to AB.

Solve the problem of finding the equations of a line perpendicular to line segment AB through point A(3, 1) and a line parallel to AB. This covers core geometry concepts such as slopes and lines, suitable for Grades 9-11.

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