thatthel in the mid-point of the line segment joining thepoints(2,0)an

1.	thatthel in the mid-point of the line segment joining thepoints(2,0)and 0,,thenshowIf 1,2 is the mid-point of the line segment joining the points (2,0) and othe showthat the line 5x+3y+2-0 passes through the point (-1,3p).
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 ) = ( 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 thepoint ( -1 , 3p ) . Like my answer if you find it useful! thanks

thatthel in the mid-point of the line segment joining thepoints(2,0)and 0,,thenshowIf 1,2 is the mid-point of the line segment joining the points (2,0) and othe showthat the line 5x+3y+2-0 passes through the point (-1,3p).

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 ) = ( 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 thepoint ( -1 , 3p ) .

Like my answer if you find it useful!

thanks