CBSE Class 10 Maths Sample Paper 2019 | Q16B

This 2019 CBSE class 10 Maths 3 mark question is from Coordinate Geometry. An easy 3 mark question which tests the concept of collinear points.

Question 16B : Find the value of k for which the points (3k-1, k-2), (k, k-7) and (k-1, -k-2) are collinear.

Video Explanation

Explanatory Answer | CBSE Sample Paper 2019 Question 16 Internal Choice 2

Property: If three points are collinear, the area of triangle formed by these points is 0.

The three points are: A(3k - 1, k - 2), B(k, k - 7) and C(k - 1, -(k + 2))
Area of triangle ⇒ \\frac{1}{2}) { x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂) }
\\frac{1}{2}) { (3k − 1)(k − 7 + k + 2) + k(−k − 2 − k + 2) + (k − 1)(k − 2 − k + 7) } = 0
{(3k² – 21k + 3k² + 6k – k + 7 – k - 2) + (-k² - 2k – k² + 2k) + (k² – 2k – k² + 7k – k + 2 + k – 7)} = 0
(6k² – 17k + 5) + (-2k²) + (5k – 5) = 0
4k² – 12k = 0
4k (k – 3) = 0
k = 0 or 3