![]() 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.180° clockwise and counterclockwise rotation: \((x,y)\) becomes \((-x,-y)\).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. So from 0 degrees you take (x, y) and make them negative (-x, -y) and then you've made a 180 degree rotation.Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point. When you rotate by 180 degrees, you take your original x and y, and make them negative. If you have a point on (2, 1) and rotate it by 180 degrees, it will end up at (-2, -1) We do the same thing, except X becomes a negative instead of Y. If you understand everything so far, then rotating by -90 degrees should be no issue for you. Our point is as (-2, -1) so when we rotate it 90 degrees, it will be at (1, -2)Īnother 90 degrees will bring us back where we started. What about 90 degrees again? Same thing! But remember that a negative and a negative gives a positive so when we swap X and Y, and make Y negative, Y actually becomes positive. Our point is at (-1, 2) so when we rotate it 90 degrees, it will be at (-2, -1) What if we rotate another 90 degrees? Same thing. So from 0 degrees you take (x, y), swap them, and make y negative (-y, x) and then you have made a 90 degree rotation. When you rotate by 90 degrees, you take your original X and Y, swap them, and make Y negative. If you have a point on (2, 1) and rotate it by 90 degrees, it will end up at (-1, 2) In case the algebraic method can help you:
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