# Introduction to the cartesian coordinate system

Suppose the index says that your target street is located at D In other words, only 5 units up.

## Coordinate plane

Cartesian Coordinate System[ edit ] The foundations of Analytic Geometry lie in the search for describing geometric shapes by using algebraic equations. And I like it just because it's very practical, and it makes you realize that these great minds, these pillars of philosophy and mathematics, at the end of the day, they really were just human beings. So that's that point right over there, 0, negative 1, right over there. Direction As x increases, the point moves further right. So me write that, 1. Abscissa and Ordinate You may hear the words "Abscissa" and "Ordinate" To show students that the coordinate plane is useful in more than just describing the location of objects lead a discussion on reading points off a graph. This information will be lost if you stick with the high-school way of splashing arrow-tips everywhere on every line. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. So let me erase this and extend this down a little bit so I can go all the way down to negative 5 without making it look too messy. And that's associated with negative 5 in the vertical direction. And let's put our independent variable, the one where I just randomly picked values for it to see what y would become, let's put that on the horizontal axis. The two axes divide the plane into four right angles , called quadrants.

That's one direction. The Cartesian coordinates of P are those three numbers, in the chosen order. I made every mistake that could be made.

## Introduction to the cartesian coordinate system

Further information: Two-dimensional space A Cartesian coordinate system in two dimensions also called a rectangular coordinate system or an orthogonal coordinate system  is defined by an ordered pair of perpendicular lines axes , a single unit of length for both axes, and an orientation for each axis. The two numbers, in that chosen order, are the Cartesian coordinates of P. The above distance formula allows us to compute the length of this segment. And we go into some depth in that in the geometry playlist. It may take some thought to verify this, but this system is inherently different from the one created by using the "left hand rule. That's that point right over there. Thus, the origin has coordinates 0, 0, 0 , and the unit points on the three axes are 1, 0, 0 , 0, 1, 0 , and 0, 0, 1. But I'll pick relatively straightforward values just so that the math doesn't get too complicated. As in the two-dimensional case, each axis becomes a number line. So I'll say that point has the coordinates, tells me where to find that point, negative 2, negative 5. This gives us a relationship between whatever x is and whatever y is.

Now, he did many things in philosophy and mathematics. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line.

### Cartesian plane graph

And that's just what people decided to do. And I could just pick random values for x, and then figure out what y is. We will focus on quadric surfaces where these coeffiecients are 0; we will not consider rotations. And he's probably most known in popular culture for this quote right over here, a very philosophical quote. And it actually was Descartes who came up with the convention of using x's and y's, and we'll see later z's, in algebra so extensively as unknown variables or the variables that you're manipulating. A line with a chosen Cartesian system is called a number line. We cannot draw three lines representing the three axes in which each line is perpendicular to the other two. So let me erase this and extend this down a little bit so I can go all the way down to negative 5 without making it look too messy. So that is 4 minus 1 is equal to 3.

When x is 2, y is 3, 2 comma 3. For any point P, a line is drawn through P perpendicular to each axis, and the position where it meets the axis is interpreted as a number. The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the first quadrant. The one variable with a positive coefficient corresponds to the axis that the cones "open'' along. There are no standard names for the coordinates in the three axes however, the terms abscissa, ordinate and applicate are sometimes used. This particular method of creating surfaces of revolution is limited. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" or "points" from the negative half towards the positive half.

### 3d cartesian coordinate system

The Coordinate System[ edit ] For a coordinate system to be useful we want to give to each point an atribute that help to distinguish and relate different points. If x is equal to 0, then y is going to be 2 times 0 minus 1. Direction As x increases, the point moves further right. The reverse construction determines the point P given its three coordinates. Quadric Surfaces Spheres, planes and cylinders are important surfaces to understand. And so we can number it. That is a solution to this equation. If x is 2, then y is going to be 2 times now our x is minus 1. One convention is that the axes must conform to the right hand rule. This requires us to complete the square three times.
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