00:01
When we write a proof using coordinate geometry, our first task is always to position the figure in the coordinate plane and to assign coordinates to the vertices.
00:12
So let's take a look at an example.
00:15
In this problem, we're going to place a right triangle in the coordinate plane, specifically a right triangle with leg lengths of m and n.
00:28
And you may be wondering, well, hey, you know, where's the numbers? how long are these? legs.
00:33
But in this case, we're actually going to be using variables for the lengths of the two legs, because if we wanted to prove a theorem about all right triangles, we don't know how long the legs are.
00:44
Maybe the legs are one unit and five units.
00:47
Maybe it's three units and ten units.
00:49
So if we want to write a proof that represents all possible right triangles, we can't pick specific numbers to represent the lengths of the legs.
00:58
We need to use variables.
01:02
So let's go ahead now and place the this right triangle in the coordinate plane.
01:08
And most of the time when we're working with right triangles, it's gonna be beneficial to place one vertex at the origin, specifically the vertex here at the right angle, because we know that in the coordinate plane, our x and our y axes meet at a right angle.
01:32
So x and y here, axes are perpendicular, making a nice right angle...