# CBSE Class 10 Maths Sample Paper 2019 | Q16B

#### Section C | Collinear Points | Coordinate Geometry

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.

## NCERT Solution to Class 10 Maths

### 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

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