Given two points A (-5, 2) and B (1, -4), find :
slope of perpendicular to AB

Answer

To find the slope of the line perpendicular to the line segment AB connecting the points A (-5, 2) and B (1, -4), we can follow these steps:

### Step 1: Identify the coordinates of points A and B
The coordinates of point A are (-5, 2) and the coordinates of point B are (1, -4).

### Step 2: Calculate the slope of line AB
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Substituting the coordinates of points A and B:
- \(x1 = -5\), \(y1 = 2\)
- \(x2 = 1\), \(y2 = -4\)

Calculating the slope:
\[ m_{AB} = \frac{-4 - 2}{1 - (-5)} = \frac{-6}{1 + 5} = \frac{-6}{6} = -1 \]

### Step 3: Use the property of perpendicular slopes
If two lines are perpendicular, the product of their slopes is -1. Let \(m_1\) be the slope of line AB and \(m_2\) be the slope of the line perpendicular to AB. Therefore:
\[ m_1 \cdot m_2 = -1 \]
Substituting \(m_1 = -1\):
\[ -1 \cdot m_2 = -1 \]

### Step 4: Solve for \(m_2\)
To find \(m_2\):
\[ m_2 = 1 \]

### Conclusion
The slope of the line perpendicular to line AB is \(1\).

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