Find the equation for the height CH Vertices of the triangle A (-1; 7) B (-3; -1) C (11; -3).

1. Let’s compose the equation of the side AB of the triangle ABC and the slope of the straight line:

Vertices A and B coordinates:

A (-1; 7);
B (-3; -1);
(y – 7) / (x + 1) = (-1 – 7) / (- 3 + 1);
(y – 7) / (x + 1) = -8 / (- 2);
(y – 7) / (x + 1) = 4;
y – 7 = 4 (x + 1);
y = 4x + 4 + 7;
y = 4x + 11;
k1 = 4.
2. The slope of the line perpendicular to the side AB and the equation for the height CH:

k2 = -1/4;
Vertex C:

C (11; -3);
y + 3 = k2 (x – 11);
y + 3 = -1/4 * (x – 11);
y = -1/4 * x + 11/4 – 3;
y = -1/4 * x – 1/4.
Answer. The equation for the height of CH is: y = -1/4 * x – 1/4.