# Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and (5k – 1, 5k) are collinear. - Mathematics

Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and (5k – 1, 5k) are collinear.

#### Solution

A(k + 1, 2k) , B(3k, 2k + 3) and (5k – 1, 5k)
If 3 points are collinear then area of triangle formed by them = 0

1/2[(k+1)(2k+3-5k)- 2k(3k-5k+1)+1(15k^2- 10k^2- 2k+ 15k - 3)= 0

1/2[-3k^2+3k-3k+3+4k^2-2k+15k^2-10k^2-2k+15k-3]=0

1/2[6k^2+11k]=0

6k^2+11k=0

k=0,-11/6

Concept: Area of a Triangle
Is there an error in this question or solution?