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).
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:
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?
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.