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Math Help - Equation of Line Through C & Midpoint

  1. #1
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    Equation of Line Through C & Midpoint

    Let A(1,2), B(6,1) and C(7,8) be three points in the plane. Find the equation of the line passing through point C and through the midpoint of the line segment AB. Write answer in the form
    ax + by + c = 0.

    I found slope of AB to be (-1/5).
    I also found the midpoint of AB to be (7/2, 3/2).

    I then decided, for unknown reasons, to calculate the slope of the perpendicular bisector to be 5.

    I then plugged 5 and the midpoint into point-slope formula and got the wrong answer. Trying a second time through guessing, I decided to plug 5 and point C into the point-slope formula and again got the wrong answer. The textbook does not give a sample representing the question above or else I can do it in 5 minutes.

    What are the steps leading to the right equation? I just want the steps to see if I can work it out alone. Thank you very much.
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    Re: Equation of Line Through C & Midpoint

    Quote Originally Posted by nycmath View Post
    Let A(1,2), B(6,1) and C(7,8) be three points in the plane. Find the equation of the line passing through point C and through the midpoint of the line segment AB. Write answer in the form
    ax + by + c = 0.
    I also found the midpoint of AB to be (7/2, 3/2).
    The mid point is M: \left( {\frac{7}{2},\frac{3}{2}} \right).

    Now find the slope determined by C~\&~M. Then write the line.
    Thanks from nycmath
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    Re: Equation of Line Through C & Midpoint

    Notice that C to Midpoint of AB is not necessarily the same as a perpendicular of AB, therefore your entire problem remains.

    Let the Midpoint of AB be M(X,Y) and you have already found that answer to be (\frac{7}{2}, \frac{3}{2})

    Finding the Gradient is easy, since we know two points on the line. \frac{8-\frac{3}{2}}{7-\frac{7}{2}}=\frac{13}{7}

    Equation of the Line (y-8)=\frac{13}{7}(x-7)

    13x-7y-35=0

    Hope this helps
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    Re: Equation of Line Through C & Midpoint

    Quote Originally Posted by Plato View Post
    The mid point is M: \left( {\frac{7}{2},\frac{3}{2}} \right).

    Now find the slope determined by C~\&~M. Then write the line.
    Thank you so much.
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    Re: Equation of Line Through C & Midpoint

    Quote Originally Posted by LimpSpider View Post
    Notice that C to Midpoint of AB is not necessarily the same as a perpendicular of AB, therefore your entire problem remains.

    Let the Midpoint of AB be M(X,Y) and you have already found that answer to be (\frac{7}{2}, \frac{3}{2})

    Finding the Gradient is easy, since we know two points on the line. \frac{8-\frac{3}{2}}{7-\frac{7}{2}}=\frac{13}{7}

    Equation of the Line (y-8)=\frac{13}{7}(x-7)

    13x-7y-35=0

    Hope this helps
    I truly appreciate it.
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