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# Introduction to the coordinate plane

## Video transcript

you are probably familiar with the notion of a number line where we can take a number and associated with a point on the number line so for example the number two I would go I would start at zero and go one two to the right and I would end up right over there what we're going to do in this video is think about how do we take two numbers and associate them with a point on a plane like this so for example you might have the two numbers three comma five how does that or how can these two numbers be represented as a point on the plane or how can these tell you where a point on the plane is so let's first get a little bit of terminology out of the way so what we have here this is often known as our coordinate plane these two numbers you could view as our coordinates let me write this down these are coordinates these black lines are known as the axes each one is an axis and the one that goes left right here this is known as the x-axis orts typically known as the x axis in the future it might be called other things and the one that goes up down in the vertical direction this is typically known as the y axis as you go further in math we might call it other things but most of the time it's going to be called the y axis so how does three comma five how do these coordinates specify a point on this plane well the way that we typically work it through the standard way that people will interpret these points it'll say alright this first coordinate this is our x coordinate this is our x coordinate you can view it as how far do we move to the right along the x axis so what you would do is you'd say all right I'm going to start right here where my axes intersect and I'm going to go 3 to the right 1 2 3 so my x coordinate says alright my point is going to be is going to be this far to the right this far the right so it's going to be somewhere on this vertical line this dotted line that I'm showing everything on this vertical line has an x coordinate of 3 now what's the y coordinate or I know I should state the second number right over here this is the y coordinate y coordinate this tells us how far do we move up so one way to think about you could start back at where the axes intersect this point is actually called the origin let me write that down that is the origin and so starting at the origin move 5 up 1 2 3 4 5 so everything on this horizontal line that I'm drawing has a y-coordinate of 5 so what point uniquely has both an x coordinate of 3 and a y coordinate of 5 well you can see where those two lines intersect right over here actually we do that same blue color that I wrote the coordinates in so this point right over here it has an x coordinate of 3 and it has a y coordinate of 5 that is the point 3 comma 5 now what is the coordinates of the origin well the origin is 0 to the right of the origin and it's also 0 above the origin so the coordinates there the x coordinate is 0 the y coordinate is also 0 let's do a few more examples so let's say that I wanted to plot the point 2 comma 5 why don't you pause this let me use a different number 2 comma 4 why don't you pause this video and think about where that point would be on this coordinate plane alright let's do it together so the first number is going to be our x coordinate it tells us how far do we move to the right so we move to to the right and then our second number says how far do we move up so let's first we're going to move to to the right and then we are going to move 4 up so you could say 1 2 to the right and then 1 2 3 4 right over there this right over here is the point 2 comma 4 notice its x-coordinate how far to the right of the origin it is that is 2 and its y-coordinate how far above the origin is that is 4 now let's go the other way around let's say that I were to give you if I were to give you this point right over here what would its coordinates be pause the video and try to figure that out all right well we know it's going to be two numbers so I'll do something comma something now the first something that's going to be our x-coordinate you could think of it what what point on the x-axis are we above you could think about how far to the right of the origin we are and you can see that your x coordinate right over here is if we just drop a vertical line straight down from that point it hits the x-axis at four so that is for another way to think about it we're one two three four to the right of the y-axis now how high are we how high above the x-axis are we well we're one above the x-axis so this is going to be 4 comma one another way to think about it if you just take a line and you go straight to the left you're going to hit the y-axis at the one right over here so the coordinates here are 4 comma 1 now just so we don't get confusing when you first learn this the main point of confusion is remembering that okay the first number is the x-coordinate the second number is the y-coordinate 1 comma 4 would be a different point 1 comma 4 would be okay 1 in the x-direction and then or in the y-direction so this is 1 comma 4 over here so it's very important to realize that the standard way of interpreting these numbers is that the first one says how far do you move to the right of the origin or how far do you move along the x axis or where are you on the x axis and the second number is how far do you move in the vertical direction or where are you relative to the Y or where are or where are you in in in the vertical direction