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).
Given: equation parallel to 3x – 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, -1).
To 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).
Explanation:
Let the Given points be A (2, 3) and B (4, − 1). Let M be the midpoint of AB.
∴ Coordinates of M
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 = 0
⇒ λ = -5
Substituting the value of λ in 3x – 4y + λ = 0, we get 3x – 4y – 5 = 0
Hence, the equation of the required line is 3x – 4y – 5 = 0.