So here we could have, C, D, and E are all collinear. You can have points be collinear, that is, they share the same line. Now this arrow here extends infinitely in that direction. And these arrows tell you, the geometry student, that it extends infinitely in this direction. But notice how I'm writing the arrows above my letters I have arrows on either side. Or if you have some sort of smaller letter over here, we can call this Line L. Now when you're labeling a line, it's key to include at least two points. So a line is going to be all the points, and we can actually select two of them to name it. And a line is set of points or, the word that you might learn later is locus, extending in either direction infinitely. So you can think of coplanar as sharing the same plane. So "co", you can think of it as a word for sharing. So two things are coplanar if they are, just like we have in the picture here, in the same plane. You could call this plane, Plane ABC.ĭefinition of coplanar: We actually can define this, is points, lines, or anything, segments, polygons in the same plane. So let's say you had a point right here: Point A, Point B, and Point C. And collinear we'll talk about in a second here, but collinear means they're not on the same line. Now you can name a plane using a single capital letter, usually written in cursive, or by three non-collinear points. Secondly, this paper actually has some thickness and a plane will not. Or if there are two differences between a sheet of paper and a plane, the first is this paper does not extend in every direction. So one way to visualize what a plane could be is to think about a sheet of paper. A plane is a flat surface that has no thickness, and it will extend infinitely in every direction. And the way that we label it is with a capital letter. A point has no size it only has a location. Now we're not really defining point, we're just describing it. So let's go back and define these as much as we can. And the third undefined term is the line. From these terms we define everything else. To be the names, but it can be otherwise, so just pay attention.There are three undefined terms in geometry. Nothing sacred about the horizontal coordinate being called ‘$x$’ and
$(x_1,y_1), (x_2,y_2)$ is that possibly irritating expression whichĪnd now is maybe a good time to point out that there is Point-slope form, since the slope $m$ of a line through two points Of course, the two-point form can be derived from the Instead, theĭescription of a vertical line through a point with horizontal Vertically, and the line can't be written that way. unless $x_1=x_2$, in which case the two points are aligned (x_2,y_2)$ can be written (in so-called two-point form) as The equation of the line passing through two points $(x_1,y_1),.The equation of a line passing through a point $(x_o,y_o)$ andĬan be written (in so-called point-slope form).Slope of a line is rise over run, meaning vertical change divided by horizontal change (moving from left to.Phrase ‘The set of points $(x,y)$ so that’ is omitted. Still, very often the language is shortened so that the And conceivably the $x,y$ mightīe being used for something other than horizontal and verticalĬoordinates. It is not strictly correct to say that $x^2+y^2=1$ is a circle, mostly because an equation is not a circle, even The set of points $(x,y)$ so that $x^2+y^2=1$ is a Here: for example, a correct assertion is It is important to be a little careful with use of language The next idea is that an equation can describe aĬurve. Purposes as well, so don't rely on this labelling! Often the horizontal coordinate is called the x-coordinate, and often the vertical coordinate is called the y-coordinate, but the letters $x,y$ can be used for many other The old-fashioned names abscissa and ordinate The horizontal coordinate and the second is the verticalĬoordinate. (and negative means go down instead of up). The two numbers tells how far up from the origin the point is (and negative means go left instead of right), and the second of To the right horizontally the point is from the origin The second step is that points are described by ordered pairs of numbers: the first of the two numbers tells how far This is indeed usually only implicit, so we don't worry about it. Implicitly, we need to choose a unit of measure for distances, but Origin, from which we'll measure everything else. The first thing is that we have to pick a special point, the Of geometric objects by numbers and by algebra. Let's review some basic analytic geometry: this is description
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