 So we've talked about a fair bit of math right now, we've done a simple algebra, we've done some real numbers and talked about prime numbers, some fractions, reducing, multiplying, subtracting. Now what we're going to do is look into the different branches that were formed early on from mathematics. Now one of the first branches that came off math when we started dealing with numbers was geometry. Now geometry was our attempt to understand the physical world around us, how things were put together, what type of shapes we were dealing with, how we could make things. If we saw something in nature when we tried to mimic it, when we tried to recreate it, we had to measure the dimensions and be able to reproduce it, to use it. For example, when we came up with the concept of the wheel, we had to actually measure, come up with the center of the wheel and measure the distances. Initially the wheel would have been a rudimentary, very simple that people started using, but once we started optimizing its potentials, we had to measure it, we had to get exact measurements. And that's geometry, us trying to relate to the physical world and find our place in reality. Now with geometry, it's sort of broken down into two segments. The first segment is just regular shapes and parallel lines, like dealing with triangles and boxes and squares. And they don't have any coordinate planes associated with them, like there's no reference point. All it is is an object in space where we measure and we want to get the area or we want to get the distance or we want to get the volume of an object. The other branch of mathematics is coordinate geometry where we put it on an actual plane with an x, y, sometimes a z-system, a z-coordinate where we're dealing with three-dimensional objects. So the two different branches that we have is basically you're dealing with your regular triangles, squares, boxes, and you're doing some simple calculations on them, like getting the area, the volume, finding out if two triangles are congruent or similar, looking at two parallel lines and trying to find out if the angles are the same and doing measurements, finding an angle in one position from the angles, you know, from another position. And the other one is coordinate geometry where we actually use a point of reference, an x and a y-coordinate system and we measure according to that point of reference and that point of reference is usually 0, 0. Now the way it works with coordinate geometry is they give you an x-axis, which is your horizontal axis, and they give you your y-axis, your vertical axis. Now the coordinate system that we came up with, just basically plain geometry, you can think of a map system, is the Cartesian coordinate system, which has an x and a y. Basically what you have is a coordinate system where the horizontal axis is called the x-axis usually and the vertical axis is called the y-axis. Now you can take this into three dimensions and you can do a z-axis going across this way, but we're going to stay away from that until we do, we're going to break all of this. Right now we're dealing with the basic geometry coordinate planes. Now with any coordinate system you have to have a frame of reference. The frame of reference for us is going to be right here. So this location here is going to be called 0, 0. And from here if you go off in this direction you're going to go in the positive x direction. If you go off in this direction you're going to go in the negative x direction. This way you're going to go in the negative y direction and this way you're going to go in the positive y direction. So you can think about this as positive x, negative x, negative y, and positive y. So if they tell you that you want to put a point at positive 2, let's call this 2 and negative 3. Well the way it works is your x coordinate system goes first. So x is first and y is second. So what you're going to do is you're going to go from 0, 0 to units this way. And you're going to go negative 3 which is 3 down. So you're going to go 1, 2, 1, 2, 3. So at the cross areas where you reach at this point is going to be 2 and negative 3. And you can do this coordinate system on any points that they give you. You can place it on a map. Now if they start talking about coordinates of 200 and negative 300, well you're not going to sit there and do little ticks every point. So it's up to you what kind of scale you put things on. So instead of making this a 1, you could make this 100 and make this one 200. So each tick moves 100 units. So the coordinate system, the Cartesian coordinate system, this is called the Cartesian coordinate system. The Cartesian coordinate system is really based on you what kind of scale you put on there depending on what you need. So let's throw on 2 or 3 points on here so you know how it's all laid out. So we have 2 and 3. We're going to forget about 200 and 300. That's too far for us the way we set it up right now. Let's go negative 5 and 6. So negative 5 and 6, we're going to go from here. So negative 5, the first one you're dealing with is the x. So you're going to go 1, 2, 3, 4, 5. That's negative 5. You know what? My arm is not going to reach up to 6 so I'm going to change up to 6. Let's make it 2. So we're going to go 1, 2. So this point here is negative 5 and 2. So that's how we're going to place points on a coordinate system. Now one of the things you do with a coordinate system is you put the points on there and then what you can do is connect up the points. So with the Cartesian coordinate system, if you want to measure something, let's say you find something that you want to recreate, the first thing you do is you put it according to a coordinate system. That way when you move it along somewhere else and you want to copy that image, you have a coordinate system you can use things as reference. Now with two points, the first thing you start doing with a coordinate system like this is connecting up the two points. Now if we're going to connect up these two points, let's do it with the orange line. Orange shop. So we're going to go... So all you need to be able to create a line is two points. Now from these two points, there's certain pieces of information you can get from it. Basically the first one and one of the most essential is the slope. So when you start dealing with the Cartesian coordinate system, what's going to happen is initially you're going to start talking about points where you're going to place them on a coordinate system and then what you're going to start doing in high school math specifically is connect up the two points and start explaining what these two points mean and what kind of information they're giving you.