Answer to Question #5167 in Analytic Geometry for pong javeng

Question

Determine in two ways whether or not the points A (-1,-1), B(4,1) and C(12, 4) lie on a straight line. Is AB + BC = AC? Is area ABC zero ?

Answer 1

If they lie on line then
Y=kx+b
-1=-k+b
1=4k+b
4=12k+b
b=k-1
1=4k+k-1=5k-1
k=2/5
b=-3/5
4=12*2/5-3/5=21/5, is not a line, so AB + BC is not equal to& AC
area ABC is for sure more then 0