# In triangle ABC, the coordinates of its vertices are known. Find the equations of the sides of a triangle

**In triangle ABC, the coordinates of its vertices are known. Find the equations of the sides of a triangle: AB; AC; BC А (0; –8), В (1; –1), С (- 9; 4)**

To find the equations for the sides of a triangle, we use the equation formula through two points: (x – x1) / (x2 – x1) = (y – y1) / (y2 – y1).

Let’s write for each side:

side AB: A (0; -8), B (1; -1).

(x – 0) / (1 – 0) = (y – (-8)) / (-1 – (-8))

x / 1 = (y + 8) / 7

7x = y + 8

y = 7x – 8

side BC: B (1; -1), C (-9; 4).

(x – 1) / (-9 – 1) = (y – (-1)) / (4 – (-1))

(x – 1) / (-10) = (y + 1) / 5

(x – 1) / (-2) = (y + 1)

x – 1 = -2y – 2

x + 1 = -2y

y = (x + 1) / (-2)

AC side: A (0; -8), C (-9; 4).

(x – 0) / (-9 – 0) = (y – (-8)) / (4 – (-8))

x / (-9) = (y + 8) / 12

x / (-3) = (y + 8) / 4

4x = -3y – 24

4x + 24 = -3y

y = (4x + 24) / (-3)