Question

find the value of k if point A(k+1,2k),B(3k,2k+3) and C(5k-1,5k) are collinear.​

Answer 1

Answer:

If the given points are collinear the area of triangle formed by these points will  be zero  

Step-by-step explanation:

(k+1, 2k) (3k, 2k+3) (5k-1, 5k)

1/2(x1y2+x2y3+x3y1)-(x2y1+x3y2+x1y3) [From area of triangle]

1/2(2k²+5k+3+15k²+10k²-2k)- (6k²+10k²+13k-3+5k²+5k)=0

1/2(27k²+3k+3)-(21k²+18k-3)=0

1/2(6k²-15k+6)=0

6k²-15k+6

On sloving this quadratic equation we get

k=2 and k=1/2

Now both values of k are correct