Given:
9x + 6y – 7 = 0 and 3x + 2y + 6 = 0 are parallel lines
To find:
The equation of the line mid-way between the givens line
Explanation:
The given equations of the lines can be written as:
3x + 2y - \(\frac{7}{3}\) = 0 … (1)
3x + 2y + 6 = 0 … (2)
Let the equation of the line midway between the parallel lines (1) and (2) be
3x + 2y + λ = 0 … (3)
The distance between (1) and (3) and the distance between (2) and (3) are equal.
Equation of the required line
3x + 2y - \(\frac{11}{6}\) = 0
⇒ 18x + 12y + 11 = 0
Hence, equation of required line is 18x + 12y + 11 = 0.
