# Have length and midpoint co-ordinates find endpoint?

• Oct 15th 2009, 07:18 PM
CrazyJax
Have length and midpoint co-ordinates find endpoint?
length is square root of 8
midpoint is (3,5)

try and explain as simple as possible please
• Oct 15th 2009, 07:32 PM
Soroban
Hello, CrazyJax!

We're missing some information.

Quote:

length is square root of 8
midpoint is (3,5)

There are infinitely many answers.
Here's one of them . . .

Code:

          |           |          *(4,6)           |        /           |        /           |      *(3,5)           |      /           |    /           |    *(2,4)           |       - - + - - - - - - - -           |
• Oct 15th 2009, 10:15 PM
earboth
Quote:

Originally Posted by CrazyJax
length is square root of 8
midpoint is (3,5)

try and explain as simple as possible please

All endpoints are placed on a circle with center M(3, 5) and radius $\displaystyle r = \dfrac12 \cdot \sqrt{8} = \dfrac12 \cdot 2\sqrt{2} = \sqrt{2}$

If the endpoint is P(x, y) then the locus of all endpoints is:

$\displaystyle (x-3)^2+(y-5)^2=2$