Question

Using the determinants show that the following points are collinear:

(i) (5, 5), (-5, 1) and (10, 7)

(ii) (1, -1), (2, 1) and (10, 8)

(iii) (3, -2), (8, 8) and (5, 2)

Answer 1

(i) The condition are given three points to be collinear, the area of the triangle formed by these points will be zero. As we know that, vertices of a triangle are (x₁, y₁), (x₂, y₂) and (x₃, y₃), then the area of the triangle is given by

On substituting the value of above formula.

On expanding along R₁

= 0

Here, area of triangle is zero.

Hence the points are collinear.

(ii) The condition are given three points to be collinear, the area of the triangle formed by these points will be zero. As we know that, vertices of a triangle are (x₁, y₁), (x₂, y₂) and (x₃, y₃), then the area of the triangle is given by

On substituting the value of above formula.

On expanding along R₁

= 0

Here, area of triangle is zero.

Hence the points are collinear.

(iii) The condition are given three points to be collinear, the area of the triangle formed by these points will be zero. As we know that, vertices of a triangle are (x₁, y₁), (x₂, y₂) and (x₃, y₃), then the area of the triangle is given by

On substituting the value of above formula.

On expanding along R₁

Here, area of triangle is zero.

Hence the points are collinear.