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Math Help - Solving problem involving equations of straight lines

  1. #1
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    Solving problem involving equations of straight lines

    Diagram 4 shows an equilateral ABCD.Given that C lies on the perpendicular bisector of AD and the equation of DC is x=5y-17


    Find
    (a) the equation of AB

    (b)the coordinates of point C

    (c)the equation of locus of a moving point such that its distance from point A is twice distance from D
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    Diagram 4 shows an equilateral ABCD.Given that C lies on the perpendicular bisector of AD and the equation of DC is x=5y-17


    Find
    (a) the equation of AB

    (b)the coordinates of point C

    (c)the equation of locus of a moving point such that its distance from point A is twice distance from D

    what've you done so far? What is the perpendicular bisector of a line segment? How do you find the middle point of a segment? Where are you stuck?
    All this is standard stuff in analytic geometry, you must have studied it: show us your effort to solve the question.

    Tonio
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  3. #3
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    Quote Originally Posted by mastermin346 View Post
    Diagram 4 shows an equilateral ABCD.Given that C lies on the perpendicular bisector of AD and the equation of DC is x=5y-17


    Find
    (a) the equation of AB

    (b)the coordinates of point C

    (c)the equation of locus of a moving point such that its distance from point A is twice distance from D
    1. Calculate the coordinates of the midpoint of AD.

    2. Calculate the slope of AD and consequently the slope perpendicular to AD.
    (Hint: 2 lines are perpendicular if their slopes satisfy m_1 \cdot m_2 = -1 )

    3. AB has the same slope as the perpendicular bisector and must pass through A.

    4. The point C is the point of intersection of the perpendicular bisector and the given line. I've got C(8, 5)
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    i) Find the mid point of AD. Let it be P.
    ii) Find the slope m of AD
    iii) Slope of CP = -1/m, because AD is perpendicular to CP
    iv) Find the equation of CP.
    v) Find the point of intersection of CP and CD. That gives you the co-ordinates of C.
    vi) Sole of AB is the same as the slope of PC.
    vii) Point A is given. Find the equation of AB.
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    can anybody show the step how to get the answer??
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    Quote Originally Posted by mastermin346 View Post
    can anybody show the step how to get the answer??

    If after reading CAREFULLY the detailed answers that you received from at least two posters you still don't know then you better go to your notes/book and read a little about this stuff, otherwise is like you're asking from someone to do your homework for you.

    Tonio
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