Given: equation is perpendicular to 5x -2y = 8 and pass through mid-point of the line segment joining (2, 3) and (4, 5).
To find:
The equation of the straight line perpendicular to 5x – 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).
Explanation:
The line perpendicular to 5x − 2y = 8 is 2x + 5y + λ = 0
Coordinates of the mid points of (2,3) and (4,5) = \(\Big(\frac{2+4}{2},\frac{3+5}{2}\Big)\) = (3,4)
∴ 6 + 20 + λ = 0
⇒ λ = -26
Substituting the value of λ,
We get 2x + 5y - 26 = 0,
Hence, the required equation of line is 2x + 5y-26 = 0.
