The vertices of a `DeltaABC` are A(1, 1), B(7, 3) and C(3, 6). State the slopr of the altitude to AB

Answer

To find the slope of the altitude to line AB in triangle ABC with vertices A(1, 1), B(7, 3), and C(3, 6), we can follow these steps:

### Step 1: Calculate the slope of line AB
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:

\[ m = \frac{y2 - y1}{x2 - x1} \]

For points A(1, 1) and B(7, 3):
- \(x_1 = 1\), \(y_1 = 1\)
- \(x_2 = 7\), \(y_2 = 3\)

Substituting these values into the slope formula:

\[ m_{AB} = \frac{3 - 1}{7 - 1} = \frac{2}{6} = \frac{1}{3} \]

### Step 2: Determine the slope of the altitude to line AB
The altitude from point C to line AB is perpendicular to line AB. If two lines are perpendicular, the product of their slopes is -1.

Let \(m_{CD}\) be the slope of the altitude (line CD). We have:

\[ m_{AB} \cdot m_{CD} = -1 \]

Substituting the slope of line AB:

\[ \frac{1}{3} \cdot m_{CD} = -1 \]

### Step 3: Solve for the slope of the altitude
To find \(m_{CD}\), we can rearrange the equation:

\[ m_{CD} = -1 \cdot \frac{3}{1} = -3 \]

### Conclusion
The slope of the altitude to line AB is:

\[ \text{slope of altitude } m_{CD} = -3 \]