r(ĺ˝š) is the midpoint of theine segmentjoining the points (2,0)and

1.	r(ĺ˝š) is the midpoint of theine segmentjoining the points (2,0)and(0,) then show391that the line 5x + 3y2point (-1, 3p.0 passes through the
Answer» Let ( x₁,y₁ = A( 2 , 0 ) , ( x₂ , y₂ ) = B ( 0 , 2/9 ) ; midpoint 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 ) .

r(ĺ˝š) is the midpoint of theine segmentjoining the points (2,0)and(0,) then show391that the line 5x + 3y2point (-1, 3p.0 passes through the

Answer»

Let ( x₁,y₁ = A( 2 , 0 ) ,

( x₂ , y₂ ) = B ( 0 , 2/9 ) ;

midpoint 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 ) .