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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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Lesson Transcript

Instructor:
*Artem Cheprasov*

In this lesson, you're going to learn about the definition and basic concept of rotation as well as how to rotate any shape about the origin in a coordinate plane. Finish up the lesson, then test your understanding with a quiz!

Stand up for me for a sec. Now, without moving from the spot you are in, turn to your left. Now turn back and face forward. Ok, now turn to where your back is.

What did you just do both of those times? You rotated! Simple as that. **Rotation** is the turning of a figure or object about a fixed point.

Why don't we explore how to rotate shapes using the concepts of a center, direction, and degrees?

First, let's define some really easy stuff. What do I mean when I say center? Well, think of the **center** as the fixed point around which something is rotated, something like a shape. Easy, right?

Ok, what do I mean by degrees? It's not about how hot or cold it is outside actually, but good guess. Very simply you can think of it as a word for the extent to which something happens, in our case a rotation. So, if we were to go back to our introductory example, where I told you to turn exactly to your left, you would've rotated 90 degrees. More mathematically, a **degree** is defined as unit of measurement of angles that is 1/360th of a complete turn (as per a circle).

There is one last thing I need to get to before we can start rotating some shapes for fun: that is the concept of direction. A rotation in the counterclockwise direction has an angle with a positive measure, meaning it's written as something like 90 degrees. A rotation in the clockwise direction has an angle with a negative measure, meaning it's something like -90 degrees.

Now that you know all of this, let's assume that the center of rotation in all of our examples is the origin of the coordinate plane in all of our examples. The origin is simply the point where the *x* and *y* axis intercept one another.

Cool, let's start then with some easy general rules.

- When rotating a shape by 90 degrees about the origin, each point (
*x*,*y*) becomes (*-y*,*x*) - When rotating a shape by 180 degrees about the origin, each point (
*x*,*y*) becomes (*-x*,'-y*)* - When rotating a shape by 270 degrees about the origin, each point (
*x*,*y*) becomes (*y*,*-x*)

That's all you need to know to rotate your very first shape! Remember, a shape is nothing more than a collection of points connected together with lines. So, we're just graphing points and connecting them together.

On your screen, you see a triangle. Rotate this triangle 180 degrees about the origin. First, let's find the coordinates of the three points of our triangle. They are (3,-1), (1,0), (2,1). Using the general rules I just discussed, they become (-3,1), (-1,0), (-2, -1). Simply place those three points on the graph, connect the dots, and presto! You've just rotated your first shape.

Ok, let's try another one. Let's rotate the original triangle, with the same starting points of (3,-1), (1,0), (2,1) by 270 degrees about the origin this time. Again, using our nifty rules from before, we get three new points for the triangle: (-1,-3), (0,-1), (1,-2). Connect the dots, and voila! You just rotated your second shape.

I know that was easy. You're now a total pro. All you have to do is remember some very simple definitions and rules and you can rotate just about any shape about the origin.

**Rotation**is the turning of a figure or object about a fixed point- The
**center**is the fixed point around which something is rotated - A
**degree**is defined as unit of measurement of angles that is 1/360th of a complete turn (as per a circle)

A rotation in the counterclockwise direction has an angle with a positive measure, while a rotation in the clockwise direction has an angle with a negative measure.

- When rotating a shape by 90 degrees about the origin, point (
*x*,*y*) becomes (*-y*,*x*) - When rotating a shape by 180 degrees about the origin, point (
*x*,*y*) becomes (*-x*,'-y*)* - When rotating a shape by 270 degrees about the origin, point (
*x*,*y*) becomes (*y*,*-x*)

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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