![]() #5: Explore what happens when the reflection is not parallel. If you first reflect the triangle over the line and then translate it, you will get a different image than if you translate it first and then reflect it. No, the order in which the transformations are applied matters. #4: Is the composition of a translation followed by a reflection (over a line parallel to the vector) the same as first reflecting over the line and then applying the translation? The combination of the two transformations creates a unique image. When you perform a glide reflection, the resulting image is not the same as if you had just done a translation, reflection, or rotation on its own. #3: Notice that this composition is not equivalent to a single translation, reflection, or rotation. Click on the triangle to reflect it over the line. Then, select the "Reflect" tool and choose a line that is parallel to the vector you used for the translation. Move the triangle to a new location by clicking on a point and dragging it to a new position. ![]() To do this, select the "Translate" tool and click on the triangle. #2: Explore what happens when the triangle is translated by a vector and then reflected by a line parallel to the vector. You can use the "Move" tool to adjust the size and shape of the triangle as needed. Click three points on the screen to create a triangle. To do this, open GeoGebra and select the "Polygon" tool. #1: Construct a generic, scalene triangle ABC in GeoGebra. #s Why is the condition (that the line of reflection is parallel to the vector) included in the definition of a glide reflection? Explore what happens when the reflection is not parallel. Note that in the definition of a glide reflection, the line of reflection must be parallel to the translation vector. #4 Is the composition of a translation followed by a reflection (over a line parallel to the vector) the same as first reflecting over the line and then applying the translation? However, since this type of isometry is defined via a composition, it is reasonable to ask if the order in which the two components are applied matters. Hence, it is given a name (Glide Reflection) and added to the list of "basic" isometries. Notice that this composition is not equivalent to a single translation, reflection, or rotation. Then explore what happens when it is translated by a vector and then reflected by a line parallel to the vector. Construct a generic, scalene triangle ABC in GeoGebra.
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