Question

Show that the points (1,2),(2,1) under (-2,5) are collinear

Answer 1

If the area of the points is 0 it is collinear.

Answer 2

• For the Points (Vertices of Triangle) to be Collinear, The Area of Triangle should be 0

Area of Triangle =  1/2 [x₁ (y₂ - y₃ ) + x₂ (y₃ - y₁ ) + x₃(y₁ - y₂)]

We have :

• x₁ = 1 , x₂ = 2 , x₃ = -2

• y₁ = 2 , y₂ = 1 , y₃ = 5

⇒ Area of Triangle =  1/2 [x₁ (y₂ - y₃ ) + x₂ (y₃ - y₁ ) + x₃(y₁ - y₂)]

⇒ Area of Triangle =  1/2 [1 (1 - 5) + 2 (5 - 2 ) + (-2)(2 - 1 )]

⇒ Area of Triangle =  1/2 [1 (-4) + 2(3)  -2(1)]

⇒ Area of Triangle =  1/2 [-4 + 6 - 2]

⇒ Area of Triangle =  1/2 [0]

⇒ Area of Triangle =  0/2

⇒ Area of Triangle =  0

As The Area of Triangle is 0, We showed the given points are collinear