Question

Find the value of k if. A (k+1, 2k) ,b (3k,2k + 3) C (5K - 1 , 5 k)

Answer 1

area of triangleABC = 0

1/2 l (x1[ y2-y1] +x2[y3-y1]+x3[y1-y2]l =0

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

so

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