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If I Ăs the midpoint ofthe lin esegment iningthepoints(2,0)andĺ˛,thenshowthattheline 5x + 3y +2 0 passes through the point (1, 3p). |
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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 =05 ( -1 ) + 3× ( 3p ) + 2 = 0-5 + 3× 3 ( 1/3 ) + 2 =0 [ from ( 1 ) ]-5 + 3 + 2 =00 = 0 [ true ]Therefore ,5x + 3y + 2 =0 line passes through thepoint ( -1 , 3p ) . |
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