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Find the coordinates of the foot of the ...

Find the coordinates of the foot of the perpendicular drawn from the point `(1,-2)` on the line `y=2x+1.`

Text Solution

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Here, slope of line, `y = 2x+1` is `2`.
`:.` Slope of lineperpendicular to this line `= -1/2`
Let foot of the perpendicular is `(x_1,y_1)`.
Then, `y_1 = 2x_1+1.`
So, from the point, `(1,-2)`,
`(2x_1+1+2)/(x_1-1) = -1/2`
`=>(2x_1+3)/(x_1-1) = -1/2`
`=>4x_1+6 = 1-x_1`
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Knowledge Check

  • The coordinates of the foot of the perpendicular drawn from the point (3,4) on the line 2x+y-7=0 are

    A
    `(9/5, (17)/5)`
    B
    (1,5)
    C
    (-5, 1)
    D
    (1, -5)

  • The coordinates of the foot of the perpendicular drawn from the point (3,4) on the line 2x +y-7 =0 are

    A
    `9/5, 17/5`
    B
    1,5
    C
    `-5,1`
    D
    1,-5

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