A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find :
the slope of the altitude of AB. 

Answer

To find the slope of the altitude from point C to line AB in triangle ABC with vertices A(5, 4), B(-3, -2), and C(1, -8), we will follow these steps:

### Step 1: Find the slope of line AB
The slope (m) of a line through two points (x1, y1) and (x2, y2) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For points A(5, 4) and B(-3, -2):
- Let (x1, y1) = (5, 4) and (x2, y2) = (-3, -2).

Substituting the coordinates into the formula:
\[ m_{AB} = \frac{-2 - 4}{-3 - 5} = \frac{-6}{-8} = \frac{3}{4} \]

### Step 2: Determine the slope of the altitude from point C
The altitude from point C to line AB will be perpendicular to line AB. The relationship between the slopes of two perpendicular lines is given by:
\[ m_1 \cdot m_2 = -1 \]
Where \(m_1\) is the slope of line AB and \(m_2\) is the slope of the altitude.

We already found that:
\[ m_{AB} = \frac{3}{4} \]
Thus, we can set up the equation:
\[ \frac{3}{4} \cdot m_{CD} = -1 \]

### Step 3: Solve for the slope of the altitude
To find \(m_{CD}\), we rearrange the equation:
\[ m_{CD} = \frac{-1}{\frac{3}{4}} = -\frac{4}{3} \]

### Conclusion
The slope of the altitude from point C to line AB is:
\[ \boxed{-\frac{4}{3}} \]