Question

points a and b have coordinates (3k-4 -2) and (1 ,k+1) respectively where k is a constant. given the gradient of AB is -3/2

Answer 1

Answer:

k = 3

Step-by-step explanation:

Hi,

If points A(x₁, y₁) and B(x₂, y₂) are given, then the gradient of AB is given by

  (y₂ - y₁)/(x₂ - x₁).

Now, given that A (3k-4, -2) and B (1, k+1)

Also gradient  = -3/2

Using the formula of gradient for AB, we get

(k + 1 + 2)/(1 - 3k + 4) = (k + 3)/(5 - 3k) = -3/2

⇒ 2k + 6 = -15 + 9k

⇒ 7k = 21

⇒ k = 3,

Hence, the value of k is 3.

Hope, it helped !