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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.
Solution
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
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