Question

determine K so that the point (k,2) (2,1) and (5,-1) are collinear​

Answer 1

Answer :

Consider the given points.(k,2),(2,1) and (5,-1)

these points are collinear means that the area of triangle must me zero.

where , ( shown above in 1st picture ) ... are the points

therefore,

$\frac{1}{2} |k(1 - ( - 1)) + 2( - 1 - 2) + 5(2 - 1)| = 0$

$\frac{1}{2} |k(2) + 2( - 3) + 5(1)| = 0$

$\frac{1}{2} |2k - 6 + 5| = 0 \\ \\ \frac{1}{2} |2k - 1| = 0 \\ \\ 2k = 1 \div \frac{1}{2} \\ \\ 2k = \frac{1}{1} \times \frac{2}{1} \\ \\ 2k = 2 \\ \\ k = 1$

Hence, this is the answer.