Question

using the distance bermula
show that the given points
are Gothe collinear
(1,-1),(5,2)and(9,5) ​

Answer 1

Answer:

The given three points are collinear.

Step-by-step-explanation:

Let the given three points be A, B & C.

• A ≡ ( 1, - 1 ) ≡ ( x₁, y₁ )
• B ≡ ( 5, 2 ) ≡ ( x₂, y₂ )
• C ≡ ( 9, 5 ) ≡ ( x₃, y₃ )

We know that,

d ( A, B ) = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]

⇒ d ( A, B ) = √[ ( 1 - 5 )² + ( - 1 - 2 )² ]

⇒ d ( A, B ) = √[ ( - 4 )² + ( - 3 )² ]

⇒ d ( A, B ) = √( 16 + 9 )

⇒ d ( A, B ) = √25

⇒ d ( A, B ) = 5 units

Now,

d ( B, C ) = √[ ( x₂ - x₃ )² + ( y₂ - y₃ )² ]

⇒ d ( B, C ) = √[ ( 5 - 9 )² + ( 2 - 5 )² ]

⇒ d ( B, C ) = √[ ( - 4 )² + ( - 3 )² ]

⇒ d ( B, C ) = √( 16 + 9 )

⇒ d ( B, C ) = √25

⇒ d ( B, C ) = 5 units

∴ d ( A, B ) = d ( B, C )

∴ The given three points are collinear.