1. If the points (2,1) and (1,-2) are equidistant from the point(x,y) show that x+3y=0 please help fast
Answers
Answer:
x + 3y = 0
Step-by-step-explanation:
Let the points be A and B.
Let P be the point equidistant from points A & B.
A ≡ ( 2, 1 ) ≡ ( x₁, y₁ )
B ≡ ( 1, - 2 ) ≡ ( x₂, y₂ )
P ≡ ( x, y )
Point P is equidistant from A and B.
∴ PA = PB
∴ By distance formula,
⇒ √[ ( x - x₁ )² + ( y - y₁ )² ] = √[ ( x - x₂ )² + ( y - y₂ )² ]
⇒ √[ ( x - 2 )² + ( y - 1 )² ] = √{ ( x - 1 )² + [ y - ( - 2 ) ]² }
⇒ √[ ( x - 2 )² + ( y - 1 )² ] = √[ ( x - 1 )² + ( y + 2 )² ]
By squaring both sides, we get,
⇒ ( x - 2 )² + ( y - 1 )² = ( x - 1 )² + ( y + 2 )²
⇒ x² - 4x + 4 + y² - 2y + 1 = x² - 2x + 1 + y² + 4y + 4
- - [ Using ( a ± b )² = a² ± 2ab + b² ]
⇒ - 4x - 2y = - 2x + 4y - - [ Cancelling equal terms from both sides with same signs ]
⇒ - 4x - 2y + 2x - 4y = 0
⇒ - 4x + 2x - 2y - 4y = 0
⇒ - 2x - 6y = 0
⇒ - 2 ( x + 3y ) = 0
⇒ x + 3y = 0 ÷ ( - 2 )
⇒ x + 3y = 0
Hence shown!
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Additional Information:
1. Distance Formula:
The formula which is used to find the distance between two points using their coordinates is called distance formula.
- d ( A, B ) = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]
2. Section Formula:
The formula which is used to find the coordinates of a point which divides a line segment in a particular ratio is called section formula.
- x = ( mx₂ + nx₁ ) / ( m + n )
- y = ( my₂ + ny₁ ) / ( m + n )
Answer:
Step-by-step explanation:
