Using determinants show that the following points are collinear:
(1, – 1), (2, 1) and (4, 5)

Question

Using determinants show that the following points are collinear: (1, – 1), (2, 1) and (4, 5)

Philoid · Accepted Answer

Given: – (1, – 1), (2, 1) and (4, 5) are three points

Tip: – For Three points to be collinear, the area of the triangle formed by these points will be zero

Now, we know that,

vertices of a triangle are (x₁,y₁), (x₂,y₂) and (x₃,y₃), then the area of the triangle is given by:

Now,

Substituting given value in above formula

R.H.S

Expanding along R₁

= 0

= LHS

Since, Area of triangle is zero.

Hence, points are collinear.

Using determinants show that the following points are collinear:(1, – 1), (2, 1) and (4, 5)