Question

for what value of k for which the points (3k-1,k-2) (k,k-7) and (k-1 ,-k-2)​

Answer 1

Answer:

k = 3

Step-by-step explanation:

Hi,

Given points are A(3k - 1, k - 2), B(k, k - 7) and C(k-1, -k - 2)

Given that A, B and C are collinear.

(*Collinearity means that all 3 points lie on the same straight line*.)

Hence, Slope of AB = Slope of AC

Slope of AB = (k - 2) - (k - 7)/(3k - 1) - k

= 5/(2k - 1)

Slope of AC = (k - 2) - (-k - 2)/(3k - 1) - (k - 1)

= 2k/2k = 1

Hence, Slope of AB should be 1

5/2k - 1 = 1

2k - 1 = 5

2k = 6

k = 3

The value of k is 3.

Hope, it helps