Have length and midpoint co-ordinates find endpoint?

**CrazyJax** · October 15th 2009, 07:18 PM

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

try and explain as simple as possible please

**Soroban** · October 15th 2009, 07:32 PM

Hello, CrazyJax!

We're missing some information.

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)
          |
      - - + - - - - - - - -
          |

**earboth** · October 15th 2009, 10:15 PM

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 $r = \dfrac12 \cdot \sqrt{8} = \dfrac12 \cdot 2\sqrt{2} = \sqrt{2}$

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

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

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