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

Step-by-step explanation:

Since, given points are collinear

Therefore, their SLOPES will be equal.

$\frac{2k + 3 - 2k}{3k - (k + 1)} = \frac{5k - (2k + 3)}{5k - 1 - 3k} \\ \therefore \: \frac{3}{3k - k - 1} = \frac{5k - 2k - 3}{5k - 1 - 3k} \\ \therefore \: \frac{3}{2k - 1} = \frac{3k - 3}{2k - 1} \\ \implies \: 3 = 3k - 3\\ \implies \: 3 + 3= 3k \\ \implies \: 6= 3k \\ \implies \: k = \frac{6}{3} \\ \implies \: \huge \fbox{ k = 2}$