Question

Find the equation of a line perpendicular to the join of A(3,5) and B(-1,7) if it passes through the midpoint of AB.

Answer 1

Let MN be perpendicular bisector of AB

`therefore` AP : PB = 1 : 1

Coordinates of P are,

P(a,b) = P`((3- 1)/2, (5 + 7)/2)` = P(1,6)

Slope of AB = `(7 - 5)/(-1 -3) = 2/(-4) = (-1)/2`

Slope of MN = 2

Equation of line MN is `("y" - "y"_1)/("x" - "x"_1)`= slope

`("y" - 6)/("x" - 1)` = 2

⇒ 2x - 2 = y - 6

⇒ 2x - y + 4 = 0

⇒ y - 2x = 4