Question

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

Answer 1

Step-by-step explanation:

The points are (1,2)( 2,1) (-2,5)

Area of a triangle =1/2 × x1(y2-y3) + x2(y3-y1) + x3(y1-y2)

= 1/2 × 1(1-5) + 2(5-2) + -2 (2-1)

= 1/2 ( 1×-4 + 2×3 + -2×1)

= 1/2 ( -4 + 6 + -2)

= 1/2 (2-2)

= 1/2 × 0 = 0

Here Area = 0 , which shows that the points are collinear

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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