Question

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

Answer 2

Hope this may help u.......


:-)