# Answer to Question #5167 in Analytic Geometry for pong javeng

Question #5167

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 ?

Expert's answer

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

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

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