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Find the equation of the straight line p...

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).

Text Solution

Verified by Experts

The line perpendicular to` 5x − 2y = 8` is `2x + 5y + lambda = 0 `
Coordinates of the mid points of `(2,3)` and `(4,5)`
` = (2+4)/2,(3+5)/2 = (3,4) `
`∴ 6 + 20 + lambda = 0`
` ⇒ lambda = -26 `
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Knowledge Check

  • The equation of the line, which is perpendicular to 5x-2y=7 and passes through the midpoint of line segment joining (2,7)and (-4,1) is

    A
    `2x+5y+18=0`
    B
    `2x=18+5y`
    C
    `2x+5y-18=0`
    D
    `5y=2x+18`

  • The equation of the straight line perpendicular to 5x-2y=7 and passing through the point of intersection of the lines 2x + 3y =1 and 3x +4y =6 is

    A
    2x+5y +17=0
    B
    2x+5y -17=0
    C
    2x -5y+17=0
    D
    2x -5y =17

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    Find the equation of the line which is perpendicular to the line 3x+2y=8 (4,-2) and passes through the midpoint of the line joining the points (6,4) and (4,-2)

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    If P(2,6) is the mid-point of the line segment joining A(6,5) and B(4,y), find y.

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