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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).
Solution
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.
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