00:01
All right, so i have two points, p and q, that are some distance apart.
00:06
And i have two points somewhere else, p prime and q prime, and they're the same distance apart.
00:13
So i can make those geometric markings.
00:15
And i want to prove that there's an isometry that takes p to p prime and q to q prime.
00:25
So to prove that there's an isometry, i can just give a set of instructions for how to construct one.
00:30
So that's what i'm going to do.
00:32
So we're allowed to translate and we're allowed to rotate.
00:35
And that's all i'm going to need.
00:37
So what i'm going to do is i'm going to translate my plane so that p lands at p prime.
00:48
So that means this gets translated over that much.
00:51
Q is going to get translated over the same amount.
00:54
So first thing i'm going to do is translate.
00:59
And i'll type that down.
01:00
So translate so that p.
01:06
Gets sent to p prime and then everything in the plane gets translated by that much okay so currently i have p is here and q is here okay now i have i've accomplished half of what i want p is at p prime i still need to get q to q prime i'm just going to accomplish that by rotation because now um we have these two line segments are the same.
01:33
There's some angle between them.
01:35
I don't know what it is...