Question

find k if a (k+1,2k), b(3k,2k+3) and c (5k-1,5k) are collinear

Answer 1

Hey mate !
________

Since points A, B and C are collinear, we have

Thus, Slope of AB = slope of BC i.e.,

=) (2k+3)-2k/3k-(k+1)  = 5k-(2k+3)/5k-1-3k

=) 3/2k-1 = 3k-3/2k-1

=) 3k = 6

=) k = 2

Thus, The value of K is 2

Hope it helps !

Answer 2

According to given sum,

Point A, B , C are collinear. so

Slope of AB = Slope of BC

$= > \: \frac{2k + 3 - (2k)}{3k - (k + 1)} = \frac{5k - (2k + 3)}{(5k - 1) - 3k}$

$= > \: \frac{3}{2k - 1} = \frac{3k - 3}{2k - 1}$

$= > \: 3 = 3k - 3$

=> 3k = 6

=> k= 2.


:-)Hope it helps u.