A variable line passes through a fixed point p

Asked by admin @ 17/08/2021 in Math viewed by 367 People

A variable line passes through a fixed point P. The algebraic

sum of the perpendiculars drawn from the points (2,0),(0.2) and (1, 1) on the line is zero. Find the coordinates ofthe point P.

Answered by admin @ 17/08/2021

Answer:

P ( 1 , 1 ).

Step-by-step explanation:

Let P be ( x₁ , y₁ ) line is y - y₁ = m ( x - x₁ )

= > m x - y ( y₁ - m x₁ ) = 0 ... ( i )

= > y₁ - m x₁ = y - m x ... ( ii )

Sum of perpendicular distance from ( 2 , 0 ) , ( 0 , 2 ) , ( 1 , 1 ) on ( i ) = 0

= > ( 2 m + y₁ - m x₁ ) / √ ( m² + 1 ) + ( - 2 + y₁ - m x₁ ) / √ ( m² + 1 ) + ( m - 1 + y₁ - m x₁ ) / √ ( m² + 1 ) = 0

= > 2 m + 3 ( y₁ - m x₁ ) - 2 + m - 1 = 0

Now using ( ii ) we get :

= > 3 ( y - m x ) + 3 m - 3 = 0

= > y - m x + m - 1 = 0

= > y - 1 = m ( x - 1 ) [ Comparing with ( i ) we get : ]

= > x₁ = 1 and y₁ = 1

Therefore , the required point P ( 1 , 1 ).

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A variable line passes through a fixed point p

Answer:

Step-by-step explanation:

Therefore , the required point P ( 1 , 1 ).

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