# Thread: Midpoint M

1. ## 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.

2. Originally Posted by sologuitar
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.

3. ## I see...

Originally Posted by masters
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.