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Math Help - Midpoint M

  1. #1
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    Midpoint M

    Show that the midpoint M of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.

    NOTE: The given points on the picture are (0, r) and (s, 0).

    See attachment.
    Attached Thumbnails Attached Thumbnails Midpoint M-midpoint-m.jpg  
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  2. #2
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    Quote Originally Posted by sologuitar View Post
    Show that the midpoint M of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.

    NOTE: The given points on the picture are (0, r) and (s, 0).

    See attachment.
    Hi sologuitar,

    Here's a way. Maybe someone has another. We'll see.

    Draw the segment from M to the origin (0, 0). Find its distance using the distance formula.

    You should find it to be \frac{\sqrt{s^2+r^2}}{2}

    Find the coordinates of the midpoint M on the hypotenuse using the midpoint formula.

    You should come up with \left(\frac{s}{2}, \frac{r}{2}\right)

    Now find the distances from M to the vertices on the hypotenuse and you'll see they're the same as the distance from M to the origin.
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  3. #3
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    I see...

    Quote Originally Posted by masters View Post
    Hi sologuitar,

    Here's a way. Maybe someone has another. We'll see.

    Draw the segment from M to the origin (0, 0). Find its distance using the distance formula.

    You should find it to be \frac{\sqrt{s^2+r^2}}{2}

    Find the coordinates of the midpoint M on the hypotenuse using the midpoint formula.

    You should come up with \left(\frac{s}{2}, \frac{r}{2}\right)

    Now find the distances from M to the vertices on the hypotenuse and you'll see they're the same as the distance from M to the origin.
    This is more a proof question than a question I would normally see on a math test.
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