Question

If (1,p/3) is the mid point 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 points (-1,3p)

Answer 1

Hi ,

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 ]

Therefore ,

5x + 3y + 2 =0 line passes through the 

point ( -1 , 3p ) .

I hope this helps you.

: )



 

Answer 2

Answer:

Step-by-step explanation:

Since (1,p/3) is the mid point of the line segment joining the points (2,0) and (0,2/9)

Therefore p/3 =0+2/9 upon 2

#p =1/3

So, the line 5x+3y+2=0 passing through the points (-1,1) as 5(-1)+3(1)+2=0

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