Equation of line perpendicular to AB and passing through C is y = - 2 x + 9 .
According to question ,
Finding midpoint of AB :
Mid - Point of A ( 2 , 0 ) and B ( 6 , 2 ) ie. C is
= [ ( 2 + 6 ) / 2 ] , [ ( 0 + 2 ) / 2 ]
= ( 4 , 1 )
Finding slope of AB ,
Slope of AB = ( 2 - 0 ) / ( 6 - 2 )
= 1 / 2 .
Slope of line perpendicular to AB = - 2
Therefore , eqn of line perpendicular to AB and passing through C
= ( y - 1 ) / ( x - 4 ) = -2
= y - 1 = -2x + 8
y = - 2 x + 9 .
Hence equation of line perpendicular to AB and passing through C is y = - 2 x + 9 .
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