![]() ![]() 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. You can know how to slide a shape using the T ( a, b ) T ( − 10, 3 ) because the first value is always the x-axis.Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point. To avoid confusion, the new image is indicated with a little prime stroke, like this: P′, and that point is pronounced “ P prime. Suppose you have Point P located at (3, 4). The original reference point for any figure or shape is presented with its coordinates, using the x-axis and y-axis system, (x,y). ![]() Reflection – exchanging all points of a shape or figure with their mirror image across a given line (like looking in a mirror) Stretch – a one-way or two-way change using an invariant line and a scale factor (as if the shape were rubber) Shear – a movement of all the shape’s points in one direction except for points on a given line (like a crate being collapsed) Rotation – turning the object around a given fixed pointĭilation – a decrease in scale (like a photocopy shrinkage)Įxpansion – an increase in scale (like a photocopy enlargement) Translation – moving the shape without any other change You can perform seven types of transformations on any shape or figure: Translations are the simplest transformation in geometry and are often the first step in performing other transformations on a figure or shape.įor example, you may find you want to translate and rotate a shape. an isometry) because it does not change the size or shape of the original figure. A translation is a rigid transformation (a.k.a. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |