Question

if the points 2, 1 and 1 -2 are equidistant from the point x, y show that X + 3 Y is equal to zero.
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Answer 1

Answer:

The value of x + 3y is zero.

Step-by-step-explanation:

Let the given points be A, B and C.

• A ≡ ( 2, 1 ) ≡ ( x₁, y₁ )
• B ≡ ( 1, - 2 ) ≡ ( x₂, y₂ )
• C ≡ ( x, y )

We have given that,

The two points A and B are equidistant from point C.

∴ d ( A, C ) = d ( B, C )

Now, by distance formula,

⇒ √[ ( x₁ - x )² + ( y₁ - y )² ] = √[ ( x₂ - x )² + ( y₂ - y )² ]

By squaring both sides, we get,

⇒ ( x₁ - x )² + ( y₁ - y )² = ( x₂ - x )² + ( y₂ - y )²

⇒ ( 2 - x )² + ( 1 - y )² = ( 1 - x )² + ( - 2 - y )²

⇒ 2² - 4x + x² + 1² - 2y + y² = 1² - 2x + x² + ( - 2 )² + 4y + y²

⇒ x² - 4x + 4 + 1 + y² - 2y = x² - 2x + 1 + 4 + 4y + y²

⇒ - 4x + 5 - 2y = - 2x + 5 + 4y

⇒ - 4x - 2y = - 2x + 4y

⇒ - 2x - y = - x + 2y - - - [ Dividing both sides by 2 ]

⇒ - 2x + x = 2y + y

⇒ - x = 3y

⇒ x = - 3y

Now, we have to find the value of x + 3y.

x + 3y

⇒ - 3y + 3y

⇒ 0

∴ The value of x + 3y is zero.

Answer 2

Step-by-step explanation:

given :

• equidistant point are = 2, 1 and 1 -2

• x, y point equal to zero = X + 3 Y

to find :

• show that X + 3 Y is equal to zero.

knowledge required :

• The distances of the point (2, 1) and (1, -2)

• from (x, y) are √(x − 2)² + (y − 1)² and

• √(x - 1)² + (y + 2)2 units respectively. According to the problem,

solution :

• √(x - 2)² + (y − 1)² =√(x − 1)² + (y + 2)²

• or, (x - 2)² + (y - 1)² = (x − 1)² + (y + 2)²

• or, - 4x + 4 - 2y + 1 = -2x + 1 + 4y +4

• or, 2x+6y=0

• or, x + 3y = 0.

thus :

• X + 3 Y is equal to = 0 is correct answer