Question

Find the value of k if A(k+1,2k) ,B (3k,2k+3), C(5k-1,5k) are collinear

Answer 1

hope it will help you

Answer 2

Answer:

The value of k are 2 and $\frac{1}{2}$

Step-by-step explanation:

Given the points A(k+1,2k), B(3k,2k+3), C(5k-1,5k)

We have to find the value of k if given above three points are collinear.

Since the points are collinear, the area formed by these points must be 0

$\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0\\\\\frac{1}{2}[(k+1)(2k+3-5k)+3k(5k-2k)+(5k-1)(2k-2k-3)]=0\\\\\\3k-3k^2+3-3k+9k^2-15k+3=0\\\\6k^2-15k+6=0\\\\6k^2-3k-12k+6=0\\\\3k(2k-1)-6(2k-1)=0\\\\(3k-6)(2k-1)=0\\\\k=2,\frac{1}{2}$

Hence, the value of k are 2 and $\frac{1}{2}$