Rotating Shapes by Degrees, Center & Direction

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  • 0:01 What Is a Rotation?
  • 0:27 Center, Degrees, Direction
  • 1:36 Rotating Shapes
  • 3:22 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

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!

What Is a Rotation?

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?

Center, Degrees, Direction

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.

Rotating Shapes

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.

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