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00:28

Evan S.

The numbers given are the coordinates of two points on a number line. State the distance between the points. $$-3 \text { and }-17$$

00:05

Amrita B.

In Exercises $5-11$ you will have to visualize certain lines and planes not shown in the diagram of the box. When you name a plane, name it by using four points, no three of which are collinear. Write the postulate that assures you that $\overrightarrow{A C}$ exists.

00:23

Classify each statement as true or false. $A, B,$ and $C$ are collinear.

00:48

A plane can be named by three or more noncollinear points it contains. In Chapter 12 you will study pyramids like the one shown at the right below. Name five planes that contain sides of the pyramid shown.

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Hey, guys. So we've talked a lot about circles. We've talked about the definition of the circle, the area, the circumference. We've talked about how to name a chord in an arc. And what a major and minor chord in a major minor our car and how to find the measure of a narc and the length of the portion of the circumference arc length. We've also talked about area sector. We're gonna finally talk about what is the equation of a circle. We've talked about the definition of a circle that is all the points in a plane, all of the points which it is drew in a plane, which is the screen that we're talking about equi distant from a point which we call the center, that equal distance is called the Radius. So let's give a little bit more meaning to this and talk about the equation of a circle. And to do that, I'm gonna go ahead and place this on a grid. I'm just about a circle centered at a point. We're gonna call that point h comma K, and I'm gonna pick a sample point on the circle. I'm gonna call the X comma y. Now, the biggest thing about a circle is that it's all of the points equidistant from that fixed point which we call the center. So we're really concerned about the radius length? Well, the distance formula is what comes in handy here. Don't you think about this? If I was gonna find the distance between HK and X come a why okay, which would be our in this case than the distance our would be the square root of X minus h squared. Plus why minus k squared. And if I were to square root both sides part of me square both sides that when I'm left with is r squared equals X minus h squared plus quantity y minus k squared. This is Theis Equation of a Circle. Yeah, this tells us two very important things. It tells us that our center is that HK and that our radius is our alright. A very simple example would be if we had 144 equals X minus three squared Plus why plus 11 squared. I would know that my center is it three negative 11 negative 11 because the definition should have a subtraction sign here so What would make a lot of plus is a negative Negative. I also know my radius is 12, because this stands for R squared guys. Now, I could draw this. I could draw 0.3 negative 11. I could go 12 up, down, left, right. Put four points, draw a circle connecting all four of those. And we have our circle. So this is the definition of a circle in terms of its coordinates and in terms of algebra versus the word definition of the locus or the set of points in the plane equal just into a fixed point, which we call the center here we're saying the algebraic definition is the radius squared is equal to X minus h, which would be the x quarter of the center quantity squared plus y minus K, which is the white corner of the center. That quantity squared. So this is a brief intro of what a circle is to find as algebraic Lee and in its coordinates,

Parallel and Perpendicular lines

Deductive Reasoning

Non Rigid Transformations (Dilations)

Polygons

Geometry Basics

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