Question

if (1,p/3) is the midpoint of the line segment joining the points (2,0) and (0,2/9) then show that the line 5x+3y+2=0 passes through the point (-1,3p).

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Answer 1

Answer:

let ( x1 , y1 ) = A( 2 , 0 ) ,

     ( x2 , y2 ) = B ( 0 , 2/9 ) ;

mid point of joining of A and B  = ( x1+ x2 /2 , y1 + y2 /2 )

( 1 , p/ 3 ) = ( 0 + 2 /2 , 0 + 2/9 / 2 )

                  = ( 1 , 1/9 )

            p/3 = 1/9

[ ∵ If ( a , b ) = ( c , d ) then a = c and b = d ]

                   p = 1/3 --- ( 1 )

according to the problem given ,

put ( -1 , 3p ) in the equation 5x + 3y + 2 =0 

⇒ 5 ( -1 ) + 3 × ( 3p ) + 2 = 0

⇒ - 5 + 3 × 3 ( 1/3 ) + 2 = 0 [ from ( 1 ) ]

⇒ - 5 + 3 + 2 = 0

⇒ 0 = 0 [ true ]

∴ 5x + 3y + 2 = 0 line passes through the point ( -1 , 3p )

Answer 2

HeYa❤️...

Answer:

$(1 .\frac{p}{3} )is \: the \: midpoint \: of \: the \: line \: segmnt \: joining \: the \: points \: (2.0) \: and \: (0 .\frac{2}{9} ).$

$\frac{p}{3} = \frac{ \frac{0 + 2}{9} }{2} = \frac{2p}{3} = \frac{2}{9} \\ \\p = \frac{1}{3}$

Hence, the line 5x+3y+2=0, passes through the point (-1,1) as 5(-1) + 3(1) +2 = 0

I hOpe It HeLpS Ya!

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