Question

Show that the point (3,2),(4,5/2),(5,3) whether collinear or not

Answer 1

Solution :-

• If the area of given points is equals to 0 , then the points are collinear otherwise they are not. Let's check

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

Here

x₁ = 3 x₂ = 4 x₃ = 5

y₁ = 2 y₂ = 5/2 y₃ = 3

Substitute values in formula

⇒ Area = 1/2 [ 3 ( 5/2 - 3 ) + 4 ( 3 - 2 ) + 5 ( 2 - 5/2 ) ]

⇒ Area = 1/2 [ 3 ( - 0.5 ) + 4 ( 1 ) + 5 ( - 0.5 ) ]

⇒ Area = 1/2 [ - 1.5 + 4 - 2.5 )

⇒ Area = 1/2 × 0

⇒ Area = 0

Area of given points is 0 . So the points are collinear

Answer 2

$\huge\pink {Hellomate}$

Refer to the attachment