Find the slope of the line perpendicular to AB if :
`A = (3, -2) and B = (-1, 2)`

Answer

To find the slope of the line perpendicular to line segment AB, we will follow these steps:

### Step 1: Identify the coordinates of points A and B
Given:
- Point A = (3, -2)
- Point B = (-1, 2)

### Step 2: Use the slope formula
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign:
- \( (x_1, y_1) = (3, -2) \)
- \( (x_2, y_2) = (-1, 2) \)

### Step 3: Substitute the values into the slope formula
Now we substitute the coordinates into the formula:
\[ m = \frac{2 - (-2)}{-1 - 3} \]
This simplifies to:
\[ m = \frac{2 + 2}{-1 - 3} = \frac{4}{-4} \]

### Step 4: Calculate the slope
Now, we calculate the slope:
\[ m = -1 \]
Thus, the slope of line AB, denoted as \( m_1 \), is \( -1 \).

### Step 5: Find the slope of the perpendicular line
For two lines to be perpendicular, the product of their slopes must equal -1. If \( m_1 \) is the slope of line AB, and \( m_2 \) is the slope of the perpendicular line, then:
\[ m_1 \cdot m_2 = -1 \]
Substituting \( m_1 = -1 \):
\[ -1 \cdot m_2 = -1 \]

### Step 6: Solve for \( m_2 \)
To find \( m_2 \):
\[ m_2 = 1 \]
Thus, the slope of the line perpendicular to line AB is \( 1 \).

### Final Answer:
The slope of the line perpendicular to AB is \( 1 \).

---