question (1 Viewer)

[highshill]

if points (-3k,1), (k-1, k-3) and ( k-4, k-5) are collinear find the value of k

 

[Mathew587]

if points (-3k,1), (k-1, k-3) and ( k-4, k-5) are collinear find the value of k

The question states that those three points are collinear i.e. that they lie on a line.
Soo to find the value of k, I would equate the gradients of (-3k,1), (k-1, k-3) to the gradient of ( k-4, k-5),(k-1, k-3) because those two should be the same if they are collinear. Then find k through algebraic manipulation

 

[Sp3ctre]

Let A(-3k,1), B[(k-1), (k-3)], C[(k-4), (k-5)]
gradient AB = (k-3-1)/(k-1+3k) = (k-4)/(4k-1)
gradient AC = (k-5-1)/(k-4+3k) = (k-6)/(4k-4)

Since A, B and C are collinear, m(AB) = m(AC)
(k-4)/(4k-1) = (k-6)/(4k-4)
(k-4)(4k-4) = (k-6)(4k-1)
4k^2 - 4k - 16k + 16 = 4k^2 - k - 24k + 6
-20k + 16 = -25k + 6
5k = -10
k = 2