Question

tell the answer please

Answer 1

If the points are collinear , then the area is zero.

Δ=12

[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]

(ii) 0=12

[(k+1)(2k+3−5k)+3k(5k−2k)+(5k−1)(2k−2k−3)]

0=(k+1)(3−3k)+3k(3k)+(5k−1)(−3)

=3k−3k2+3−3k+9x2−15k+3

−3k2+9k2−15k+6=0

=> 6k2−15k+6=0

or 2k2−5k+2=0

2x2−4x−k+2=0

2k(k−2)−1(k−2)=0

(2k−1)(k−2)=0

Hence k=12

or k=2