1.

In each of the following find the value of 'k', for which the points are collinear. (7,-2), (5, 1), (3, k)​

Answer»

Answer

The value of k is 4

Step by step explanation

Let us consider A(7,-2) , B (5 ,1) and C(3 , k)

Given the points A , B and C are collinear so

the gradients of the LINE AB will be equals to the gradient of the line BC

Gradient of AB ,

m₁ =(y₂ - y₁)/(x₂ - x₁)

⇒m₁ = {1 - (-2)}/(5 -7)

⇒m₁= -3/2

ᵃnd the gradient of BC,

m₂ = (y₂ - y₁)/(x₂ - x₁)

⇒m₂ =(k - 1)/(3 - 5)

⇒ m₂ = -(k -1)/2

since the gradients of AB and BC are equal so

m₁ = m₂

⇒-3/2 = -(k -1)/2

⇒-3 = -(k - 1)

⇒3 = k - 1

⇒k = 4



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