can you please show me how to proof that:

if p1(x1,x2) , p2(y1,y2) then the coordinate of Midpoint is

((x1 + x2)/2 ,(y1 + y2)/2).

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- Apr 26th 2009, 04:37 PMrazemsoft21Midpoint formula (proof) ??
can you please show me how to proof that:

if p1(x1,x2) , p2(y1,y2) then the coordinate of Midpoint is

((x1 + x2)/2 ,(y1 + y2)/2). - Apr 26th 2009, 05:58 PMReferos
Ok, here's a little help: You have two points, say, A and B, with a mid-point M. Let AB be the hypotenuse of a right triangle. Thus:

http://img15.imageshack.us/img15/9176/triangleipp.png

Knowing that triangles MAK and BAC are congruent and that the length of the hypotenuse of BAC is double the hypotenuse of MAK (since M is the midpoint), can you continue the proof now? - Apr 26th 2009, 11:59 PMaidan
- Apr 27th 2009, 02:15 PMReferos
MS Paint ;D You can make perfect squares/circles and perfectly straight lines by holding shift when drawing.

- Apr 27th 2009, 04:43 PMrazemsoft21
can you help me with full answer ?

thans ! ! ? - Apr 27th 2009, 05:06 PMPlato
- Apr 27th 2009, 06:15 PMReferos
Hmm, I might be over complicating this problem, then. I was thinking something like this to prove the x-coordinate for the midpoint (I am assuming that point A is and B is ):

(triangle equality)

(because M is the midpoint)

The point C has the same x-coordinate as B. Thus its length is (the x-coordinate of C minus the x-coordinate of A)

This is the length of AK. But its length can also be expressed as the x-coordinate of K (let's call it ) minus the x-coordinate of A.

And the x-coordinate of K is the same of M.

By a similar logic, the y-coordinate of M can also be established. - Apr 28th 2009, 04:34 AMrazemsoft21
- Apr 28th 2009, 05:32 AMrazemsoft21
Marvellous Referos, GOOD JOB

Thanks a lot (Clapping)