Lucky for us, these experiments have allowed mathematicians to come up with rules for the most common rotations on a coordinate grid, assuming the origin, (0,0), as the center of rotation. In our second experiment, point A (5,6) is rotated 180° counterclockwise about the origin to create A’ (-5,-6), where the x- and y-values are the same as point A but with opposite signs. In our first experiment, when we rotate point A (5,6) 90° clockwise about the origin to create point A’ (6,-5), the y-value of point A became the x-value of point A’ and the x-value of point A became the y-value of point A’ but with the opposite sign. Let’s take a closer look at the two rotations from our experiment. Here is the same point A at (5,6) rotated 180° counterclockwise about the origin to get A’(-5,-6). Let’s look at a real example, here we plotted point A at (5,6) then we rotated the paper 90° clockwise to create point A’, which is at (6,-5). If you take a coordinate grid and plot a point, then rotate the paper 90° or 180° clockwise or counterclockwise about the origin, you can find the location of the rotated point. Let’s start by looking at rotating a point about the center (0,0). Here is a figure rotated 90° clockwise and counterclockwise about a center point.Ī great math tool that we use to show rotations is the coordinate grid. We specify the degree measure and direction of a rotation. The angle of rotation is usually measured in degrees. The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. Another great example of rotation in real life is a Ferris Wheel where the center hub is the center of rotation. A figure can be rotated clockwise or counterclockwise. A figure and its rotation maintain the same shape and size but will be facing a different direction. We call this point the center of rotation. More formally speaking, a rotation is a form of transformation that turns a figure about a point. There are other forms of rotation that are less than a full 360° rotation, like a character or an object being rotated in a video game. The wheel on a car or a bicycle rotates about the center bolt. The earth is the most common example, rotating about an axis. That's it.Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point. And last time if I draw this right here this would be a right angle And I've rotated it 90°. They're rotating it this way I have negative to positive three. So before I even graph it, I could do this so negative two And it would be positive three. Alright and my last one and read and again we're using this format. So negative four and then my value needs to be negative. And again if I draw my little lines, This would be a 90° angle So I flipped them. Okay, so I'm going to end up with negative for -2. The second point, we're going to do the same thing. My new coordinate from my greenpoint is going to be three negative three. So If I rotate it 90° and I can draw my little line here, here's my 90°. Well this makes it pretty easy because both or both numbers are three. So we're going to start with my green And all we're doing is we're rotating at 90° this way. Okay, the rule that we have is that X and Y goes two Y negative X. So for some reason it's what then just go the opposite direction. So they asked us to do that for each point and we're going to give the new point and that we're given so pre image and image and I'm taking these as the pre image and because those are the coordinates that they gave us. So just what that means is if we were looking at just the straight up line, We are going to the right so clockwise and we're going to go 90°. So in this question were given three points And were asked to do a 90° clockwise rotation.
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