00:01
In this problem, we're going to prove that the midpoint, so we have p1 and p2, that p, we're going to say m for midpoint, is x1 plus x2 over 2, y1 plus y2 over 2, and z1 plus z2 over 2.
00:21
So for space and time, we know if we just prove the x component, that it will also prove.
00:30
We could go through the same process to prove the y and the z, but it gets really messy if you do it all.
00:34
So we're just going to do it in terms of x.
00:37
So we're going to use the distance formula and prove that p1, p2, the distance of that divided by 2 is equal to the distance from p1 to pm.
00:49
Okay.
00:50
So again, we're just going to do it in the x.
00:52
Direction so p1 p2 is x1 minus x2 it would be squared you take the square root of that and the whole thing is divided by 2 this is equal to p1 is x1 minus p m is x1 plus x2 over 2 this whole thing is squared in the square root of that so these should be equal if if this, to prove this midpoint.
01:30
So we're going to square both sides.
01:32
So we get x1 minus x2 squared over 4 equals x1 minus x1 plus x2 over 2.
01:42
That whole thing's squared...