Question

Determine whether the given set of points in each case are collinear or not.
(i) (7,-2),(5,1),(3,4)
(ii) (a,-2), (a,3), (a,0)​

Answer 1

The two set of points are collinear.

Rules:

Three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) are collinear if the area of the area of the triangle presumed to have formed by them is zero.

i.e., x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂) = 0

Step-by-step explanation:

(i)

Here the three points are (7, - 2), (5, 1) and (3, 4)

Using the above formula, we write

7 (1 - 4) + 5 (4 + 2) + 3 (- 2 - 1)

= 7 (- 3) + 5 (6) + 3 (- 3)

= - 21 + 30 - 9

= 0

Thus the given points are collinear.

(ii)

Here the three points are (a, - 2), (a, 3) and (a, 0)

Using the above formula, we write

a (3 - 0) + a (0 + 2) + a (- 2 - 3)

= a (3) + a (2) + a (- 5)

= 3a + 2a - 5a

= 0

Thus the given points are collinear.