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.

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- Dec 14th 2009, 12:42 PMsologuitarMidpoint 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. - Dec 14th 2009, 01:35 PMmasters
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 $\displaystyle \frac{\sqrt{s^2+r^2}}{2}$

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

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

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. - Dec 14th 2009, 04:01 PMsologuitarI see...