![]() Now that we know how to rotate a point, let’s look at rotating a figure on the coordinate grid. 270° counterclockwise rotation: (x,y) becomes (y,-x)Īs you can see, our two experiments follow these rules.270° clockwise rotation: (x,y) becomes (-y,x).180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).90° counterclockwise rotation: (x,y) becomes (-y,x).90° clockwise rotation: (x,y) becomes (y,-x).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. ![]() Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point. ![]()
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