Question

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

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 !

Answer 2

Answer:

k= 3

Step-by-step explanation:

collinear means that all points lie on the same straight line ,

Hence ,slope of AB= stop of AC

slope of ABis = (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 AB should be 1

5/2k -1=1

2k-1=5

2k=6

k=3

the value of k is 3