In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.

Explanation

To find the equation and length of the altitude from vertex A in triangle ABC with vertices A(2, 3), B(4, -1), and C(1, 2), we can follow these steps:

### Step 1: Find the equation of line BC
To find the equation of line BC, we first need the slope of line BC. The coordinates of points B and C are B(4, -1) and C(1, 2).

**Slope (m) of line BC**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-1)}{1 - 4} = \frac{3}{-3} = -1
...