Question

If the points A(k+1,2k),B(3k,2k+3) and C(5k-1,5k) are collinear, then find the value of k.

Answer 1

given A(k+1,2k) ,B(3k,2k+3) ,C(5k-1,5k)

therefore
1/2l(k+1)[2k+3-5k]+3k[5k-2k]+(5k-1)[2k-(2k+3)]l=0

(k+1)[3-3k]+3k*3k+(5k-1)(-3)=0
3k-3k²+3-3k+9k²-15k+3=0
6k²-15k+6=0
divide each term with 2
2k²-5k+2=0
2k²-4k-k+2=0
2k(k-2)-(k-2)=0
(k-2)(2k-1)=0
k-2 =- or 2k-1 =0
k=2 or k= 1/2