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Question

Find the equation to the straight line parallel to 3x − 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, −1).

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Solution

Let the given points be A (2, 3) and B (4, −1). Let M be the midpoint of AB.

Coordinates of M=2+42, 3-1 2 =3, 1

The equation of the line parallel to 3x − 4y + 6 = 0 is 3x-4y+λ=0

This line passes through M (3,1).

9-4+λ=0λ=-5

Substituting the value of λ in 3x-4y+λ=0, we get 3x-4y-5=0, which is the equation of the required line.

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