If the point A(x,y) B(3,6) C(-3,4) are collinear, show that x-3y+15 = 0
Collinear means they lie on the same straight line and the gradient of AB = Gradient of BC
Gradient of BC = (6 - 4) / ( 3 - -3) = 2/6 = 1/3
Gradient of AB = (y - 6) / (x - 3) = 1/3
y - 6 = 1/3 (x - 3)
y - 6 = 1/3x -1
y - 5 - 1/3x = 0 (Multiply through by -3)
-3y + 15 + x = 0 (Re-arrange)
x - 3y + 15 = 0 (Shown)
Gradient of BC = (6 - 4) / ( 3 - -3) = 2/6 = 1/3
Gradient of AB = (y - 6) / (x - 3) = 1/3
y - 6 = 1/3 (x - 3)
y - 6 = 1/3x -1
y - 5 - 1/3x = 0 (Multiply through by -3)
-3y + 15 + x = 0 (Re-arrange)
x - 3y + 15 = 0 (Shown)
