Question

The value of k for which the point A(0,1) B(2,k) C(4,-5) are the collinear is

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of k is -2.

Given,

Three points: A(0,1), B(2,k), and C(4,-5).

To Find,

The value of k.

Solution,

As we know, for three points to be collinear the slope of the line joining two points must be equal to the slope of the line joining another two points.

⇒ Slope of AB = Slope of BC

⇒ (y₂ - y₁)/(x₂ - x₁) = (y₃ - y₂)/(x₃ - x₂)

⇒ (k - 1)/(2 - 0) = (-5 - k)/(4 - 2)

⇒ (k - 1)/2 = (-5 - k)/2

⇒ k - 1 = -5 - k

⇒ k + k = -5 + 1

⇒ 2k = -4

⇒ k = -2

Hence, the value of k is -2.

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