find value of k for which points (3k-1,k-2), (k,k-7) and (k-1,k-2) are collinear
Answers
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.
Answer:
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.