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Math Help - Finding the equation of the Median to the Hypotenuse given the coordinates of three v

  1. #1
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    Finding the equation of the Median to the Hypotenuse given the coordinates of three v

    I'm having trouble on a math problem. The problem is:
    "The coordinates of the vertices of an isosceles right triangle are (5,0),(0,0) and (0,5). Find the equation of the median to the hypotenuse"

    I know the answer, but I don't know how to write the solution and my teacher is very strict when it comes to writing the complete solution.

    I'd prefer to have the explanations rather than the answer itself. To learn and add a little challenge.

    Answers are greatly appreciated.
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  2. #2
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    Re: Finding the equation of the Median to the Hypotenuse given the coordinates of thr

    Quote Originally Posted by RPSGCC733 View Post
    I'm having trouble on a math problem. The problem is:
    "The coordinates of the vertices of an isosceles right triangle are A(5,0), B(0,0) and C(0,5). Find the equation of the median to the hypotenuse"

    I know the answer, but I don't know how to write the solution and my teacher is very strict when it comes to writing the complete solution.

    I'd prefer to have the explanations rather than the answer itself. To learn and add a little challenge.

    Answers are greatly appreciated.
    1. Draw a sketch!

    2. The vertex with the right angle is the origin of the coordinate system.

    3. The median is the straight line which connects the vertex B (that's where the right angle is located) and the midpoint of \overline{AC}.

    4. Determine the coordinates of the midpoint of \overline{AC}. You should come out with M_{AC}\left(\frac52, \frac52  \right)

    5. Now determine the equation of the line passing through the origin and the M.

    6. Draw this line into the sketch of #1 and check if your calculations are OK.
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  3. #3
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    Re: Finding the equation of the Median to the Hypotenuse given the coordinates of thr

    Find the middle of the hypotenuse and use this equation of the line that goes through (0, 0) and the middle point you found.
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    Re: Finding the equation of the Median to the Hypotenuse given the coordinates of thr

    Thank you for the quick answer. Our teacher told us to solve it without a graph, but step 5 of your answer gave me an idea.
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  5. #5
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    Re: Finding the equation of the Median to the Hypotenuse given the coordinates of thr

    This is fairly straight forward "by symmetry". The origin, (0, 0) has x and y coordinates the same. The point midway between (5, 0) and (0, 5) also has x and y coordinates the same. Therefore the equation of the line is:
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