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)

∴ 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.