In a triangle with vertices A (4, -14) B (12, -8), find the length of the height dropped from vertex C to side AB.

In the problem, the coordinates of the point C are not indicated, we denote them (c1; c2).

The vector AB will be equal to ((12 – 4); (-8 – (-12)) = (6; 4). Let’s denote the point of intersection of the height and AB by D, then the coordinates of the vector СD are equal: ((x – c1); ( y – c2) Since AD is perpendicular to AB, we get the equation CD:

6 * (x – c1) + 4 * (y – c2) = 0.

The length of the height will be equal to:

| CD | = √ (x – c1) ^ 2 + (y – c2) ^ 2.