Question

If x + 3y = 16 is the perpendicular bisector of AB and A(5, 7), then B =

Answer 1

it is given that x + 3y = 16 is the perpendicular bisector of AB where A (5, 7)

we have to find the co-ordinates of point B.

as x + 3y = 16 is perpendicular on AB, slope of lines must be -1.

i.e., slope of {x + 3y = 16} × slope of AB = -1

⇒-1/3 × slope of AB = -1

⇒slope of line AB = 3

let point B = (x, y)

then, slope of AB = (y - 7)/(x - 5)

(y - 7)/(x - 5) = 3

⇒y - 7 = 3x - 15

⇒y - 3x + 8 = 0...........(1)

now middle point of AB =[ (x + 5)/2 , (y + 7)/2] this point lies at one end of the line x + 3y = 16

so, putting it on x + 3y = 16

⇒(x + 5) + 3(y + 7) = 32

⇒x + 3y = 6 .........(2)

from equations (1) and (2) we get,

y = 1, x = 3

therefore co-ordinate of point B = (3,1)