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Lesson 99: Intro to Geometric Transformations
In this lesson, we'll take a look at the basics of geometric transformations: rotations, dilations, reflections, and translations.
This lesson reviews some concepts that we've already seen, but we'll now talk about them in a bit more detail. In geometry, we often take a shape on a coordinate plane, and then do something special with it. These special things are called transformations, and there are several different types.
Look at the example at right. We're taking a triangle, and we're doing a reflection. We're reflecting it over a vertical line. The line acts as a mirror would. In this example, the line happens to be the y-axis, but later you'll learn how to work with reflections in other lines, such as horizontal or diagonal lines.
In this example, we are taking a triangle, and doing a rotation around a point. In this example, we rotated the upper triangle 90° counterclockwise, but there are many other types of rotations which you'll learn about later.
In this next example, we've done a dilation on the triangle. That means we've enlarged it. In this example, each the x and y values of each vertex have been doubled. A dilation can also make a figure smaller. Note that we haven't rotated it or reflected it. We just enlarged it. A dilated figure is always similar to the original figure.
In this example, we've done a translation on the triangle. All we did was shift it to a new location. We didn't enlarge it, nor rotate it, nor reflect it.
Note that when we label the vertices of a figure that has undergone a geometric transformation, we put an apostrophe after each vertex letter, which is read as "prime."
Later you will learn how to work with these transformations using actual coordinates, and you'll learn methods that will make it easy to compute the coordinates of figures after a given transformation has been applied. For now, just memorize the terms presented in this lesson, and make sure that you understand the general concepts.