![]() ![]() K= Vertical Shift (add (+) when moving up, subtract (-) when moving down) Horizontal Translation: H=Horizontal Shift (add (+) when moving right, subtract (-) when moving left) In the translation example above, we go start at square ABCD and translate each coordinate of the original square ABCD 6 units to the right and 2 units up to get our new transformed image square A |B |C |D |. Remember that this type of transformation is a rigid transformation, meaning the line or shape is translated, the length, area and angles of the line and/or shape are unaffected by the transformation. Translations: When we take a shape, line, or point and we move it up, down, left, or right. Now that we know which types of transformations mainatin rigid motion, let’s explore each type of transformation in more detail! Translations: ![]() Rigid transformations include Translations, Reflections, and Rotations (but not Dilations). When a line or shape is transformed and the length, area and angles of the line and/or shape are unaffected by the transformation, it is considered to have Rigid Motion. Rigid Transformations:īefore we dive into our first type of transformation, let’s first define and explore what it means when a transformation maintains Rigid Motion. (4) Dilations (make it bigger or smaller) Shape Transformation:ġ) Translations – When we take a shape, line, or point and we move it up, down, left, or right.Ģ) Reflections – When a point, a line segment, or a shape is reflected over a line it creates a mirror image.ģ) Rotations – When we take a point, line, or shape and rotate it clockwise or counterclockwise, usually by 90º,180º, 270º, -90º, -180º, or -270º.Ĥ) Dilations – When we take a point, line, or shape and make it bigger or smaller, depending on the Scale Factor. The shape or line in question is usually graphed on a coordinate plane. Basically, when we have a shape or line and we mess around with it a bit, it is a transformation. Transformations: When we take a shape or line and we flip it, rotate it, slide it, or make it bigger or smaller. ![]() Let’s break down each of our new words before our brains explode: A translation is a type of transformation. Even the words “transformation “and “translation” can get confusing to us humans, as they sound very similar. Mathematical Transformations, include a wide range of “things.” And by “things” I mean reflections, translations, rotations, and dilations Each fall under the umbrella known as “transformations.” Alone any one of these is not difficult to master but mix them together and add a test and a quiz or two and it can get confusing. We’ll also take a look at where you might use and see transformations in your everyday life! Hope you are ready, take a look below and happy calculating! □ What is a Transformation in Math? If you like art or drawing, this is a great topic where we’ll have to use our artistic eye and our imagination for finding the right answer. There are also specific coordinate rules that apply to each type of transformation, but do not worry because each rule can also be easily derived (except for those tricky rotations, keep an eye out for those guys!). So from 0 degrees you take (x, y) and make them negative (-x, -y) and then you've made a 180 degree rotation.Hi everyone and welcome to another week of MathSux! In today’s post, we are going to go over all the different types of shape transformations in math that we’ll come across in Geometry! Specifically, we’ll see how to translate, reflect, rotate, or dilate a shape, a line, or 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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