Question

7. Find the value of k if the points A(2, 3), B(4. k) and C(6.-3) are collinear.​

Answer 1

Answer:

• k = 0

Step-by-step explanation:

Given:

• A(2, 3), B(4, k), and C(6, -3) are collinear.

To Find:

• Value of k.

We know that,

=> 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] = 0

Where,

• x₁ = 2 and y₁ = 3
• x₂ = 4 and y₂ = k
• x₃ = 6 and y₃ = -3

Now, put the values.

=> 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) = 0

=> 1/2[2(k + 3) + 4(-3 - 3) + 6(3 - k) = 0

=> 2k + 6 + 4(-6) + 18 - 6k = 0

=> 2k + 6 - 24 + 18 - 6k = 0

=> - 4k = 0

=> k = 0