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math

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(a)Given the points P(3,5),Q(8,10)and R(8,0),find the equation of a line which is perpendicular to QR and passes through the mid point of QR.
(b)The line 2x+3y=2 and 7x-3y=10 intersect at A . Find the equation of the line which passes through A and is perpendicular to the line 3x-4y=7

  • math - ,

    a) let M(8,5) be the midpoint of QR.
    QR is a vertical line, so its slope is undefined.
    A line perpendicular to QR must be a horizontal line
    A horizontal line through M(8,5) is imply
    y = 5
    (Where does point P enter the picture ? )

    b) Add the two equations ...
    9x = 12
    x = 12/9 = 4/3
    sub into the first ...
    8/3 + 3y = 2
    3y = -2/3
    y = -2/9
    point A is (4/3 , -2/9)

    The new line is to be perpendicular to
    3x - 4y = 7
    So it must have the form 4x + 3y = C
    but (4/3 , -2/9) lies on it, so
    16/3 - 6/9 = c
    times 9 ....
    48 - 6 = 9c
    c = 14/3

    we have 4x + 3y = 14/3
    or
    12x + 9y = 14

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