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The Coordinate Plane - Overview

In mathematics, the Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. The origin (0,0) is usually located at the center of the grid formed by the points, but in some contexts (such as graphing) it is useful to define the coordinates so that the origin is "outside" the grid, allowing the coordinates to be interpreted as relative distances from the origin. The two perpendicular axes are called the "axes" of the Cartesian coordinate system, and the points where they meet are its "intercepts". The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

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So in this unit we're going to shift our focus to graphic. So the most basic graphing that you'll end up doing and you'll do this a lot throughout your mathematical career is dealing what was called the coordinate plain. Well, essentially, what the coordinate plain is is a two dimensional figure, as you can see off here. To the right. Well, the Cornett plane is formed by the intersection of two axes, which are the X axis and the Y axis. Now, as you can see, your X axis is the one that's horizontal. It goes straight across. So if we were to define the X axis is the horizontal axis in our coordinate plain. But we'll just put it here as the horizontal axis and your Y axis. Well, that's the vertical axis. So the intersection of these two horizontal vertical axis That's what makes our coordinate plain well that point where these two actually crosses called the origin. That's our next vocab word. So origin is the point where the X axis and why access intersect. So that's right here in the middle. So this point right here, that would be our origin. Okay, Well, our next definition is what's an ordered pair? Well, an ordered pair is any point that's found throughout the coordinate plain. So let me get rid a that new box here. So in order pair is a point in the coordinate plain, so there's millions of them. So the very important part about what repairs is being able to define what they are and what they mean because one thing you're going to be able to dio is to plot what repairs. Or if you're given an ordered pair on the corn, the plane, you should be able to label it's court. So when we do order cares they're going to go in the order of X. And then why? So this first one is called our X coordinate, so that's going to describe the horizontal distance across from zero. So the X one is going to be our X coordinate. So this is our X coordinate, which obviously vice versa, are why value the second number in that order pair describes the Y coordinate, and the white coordinate tells us how far we are up or down vertically, away from zero the origin. So again, the X coordinate tells us how much to go left to right, left of your negative right of your positive and the white corn that tells us how much to go up or down, down if it's negative up of its positive. And in the next couple of examples, you will see how we can plot points or like I mentioned before. If you're given the coordinate plain and you need Thio, identify what the corn that iss. Okay, now, for the last definition that we're gonna have here, it's what's a quadrant? Well, quadrant has that, um, term quad in it, which means four. So a quadrant is one of the four, um, sections that the two axes create when they intercept. So it's the sections that are created by the X axis. What's more, Yeah, and why axis intersecting? I'll put them note here. There are four of them now, when we go ahead, what we're gonna do is we're gonna find that we're gonna actually label these quadrants, so let's take a look at the top. Right? So know this. If I'm going to be any coordinate in this top right section, that would mean I would go to the right and then up, meaning my X and Y coordinates are both positive. So in terms of their ordered pairs, it would be a positive number, followed by a positive number. And this top quadrant right here. This is quadrant one. And when we label our quadrants, we use Roman numerals. So now let's go to the top left. No, this R X values and negative because we wouldn't left left. But our y values air positive because we would have to go up to get to any of these points. So any point in this in this top left quadrant has a negative X value on the positive y value. And this quadrant is known as the second quadrant. Okay, let's go right below the second quadrant. Notice we would have to go left, which means our ex horn it would be negative, and we'd have to go down. Which means our Y coordinate is also negative. So this quadrant here, where your X and Y values are both negative, this is known as you're 30 quadrant. All right, Now, for the last question we haven't talked about notice you would go right. Which on your X axis, we means your ex values are positive, but then you would have to go down, which means you're wide values or negative. So for all of these ordered pairs, your ex would be positive and your wife would be negative. And this is known as your four quadrant. So, like I said, any time you're asked to identify quadrants, you wanna use the Roman numerals. So in the next couple of examples, what we're going to do is we're going to talk about how to label ordered pairs if you're given the order parent to plot it. If you're given the graph and you're asked to identify ordered pairs, um, to be able to identify quadrants if you're just given the order parent, you're not actually given the visual of the graph, and then we'll also, in the very last example, start discussing how coordinate planes or the idea of plotting points can be useful, especially when it comes to data. So that's what you're gonna find in the next couple of examples

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Top Algebra Educators
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Missouri State University

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Oregon State University

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