Question

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).

Answer 1

5x - 2y = 8
2y = 5x - 8
⇒ y = `(5)/(2) x - 4`
y = mx + c
∴ m₁ = `(5)/(2)`
Since lines are perpendicular to each other
∴ m₁ x m₂ = -1
`(5)/(2) xx m_2` = -1
m₂ = `-1 + (2)/(5)`
m₂ = `-(2)/(5)`
Coordinates of midpoints
= `(2 + 4)/(2),(3 + 5)/(2)`
Passing Point = (3, 4)
∴  Equation of line,
y - y₁ = m(x - x₁)
⇒ y - 4 = `(-2)/(5)(x - 3)`
⇒ 5y - 20 = -2x + 6
⇒ 2x + 5y = 26.