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)