# GeoGebra Lab #4: Transformations

## Construction #1: Translations

Follow the instructions provided below to create a GeoGebra applet that translates a polygon.

## Instructions

Step 1: On the right side of the applet (or, on the right side of the axes) draw a non-regular, non-symmetric 5+ sided polygon using the Polygon tool. (That is, a polygon with 5 or more sides that doesn't look too neat and tidy!)
Step 2: On the left side of the applet (or, on the left side of the axes), draw a vector using the vector tool.
Step 3: Use GeoGebra's inbuilt "Translate by vector" tool. Be sure to read the tool tips that show up when you select this tool!
Step 4: Make changes to the polygon and to the vector to see how those changes affect the translated image.

## Construction #2: Reflections

Follow the instructions provided below to create a GeoGebra applet that reflects a polygon.

## Instructions:

Step 1: Draw a non-regular, non-symmetric 5+ sided polygon using the Polygon tool. (That is, a polygon with 5 or more sides that doesn't look too neat and tidy!)
Step 2: Draw the line of reflection using the line tool.
Step 3: Use GeoGebra's inbuilt "Reflect about line" tool, to reflect your polygon.
Step 4: Make changes to the polygon and to the line of reflection to see how those changes affect your reflected image.

## Construction #3: Rotations

Follow the instructions provided below to create a GeoGebra applet that rotates a polygon.

## Instructions

Step 1: Draw a non-regular, non-symmetric 5+ sided polygon using the Polygon tool. (That is, a polygon with 5 or more sides that doesn't look too neat and tidy!)
Step 2: Plot a point (NOT ON THE POLYGON) about which you will rotate.
Step 3: To mark the angle of rotation, we will use the slider tool. In the menu that pops up, make sure your slider is set to "angle," goes from 0

^{o}to 360^{o}, with an increment (step size) of 5^{o}. Step 3: Use GeoGebra's inbuilt "Rotate around point" tool to rotate your polygon. When GeoGebra asks the angle by which to rotate, put in , which should be the name of your angle, by clicking the Greek menu at the end of the input box. Step 4: Make changes to the polygon, the point of rotation, and the slider angle to see how those changes affect your rotated image.## Construction #4: Dilations

Follow the instructions provided below to create a GeoGebra applet that dilates a polygon.

## Instructions

Step 1: Draw a non-regular, non-symmetric 5+ sided polygon using the Polygon tool. (That is, a polygon with 5 or more sides that doesn't look too neat and tidy!)
Step 2: We will again use the slider tool, this time to define the scale factor by which we will dilate. In the menu that pops up, make sure your slider is set to "number" and goes from 0 to 5 with an increment of 0.1.
Step 3: Use GeoGebra's inbuilt "Dilate from point" tool to dilate your polygon. Select your polygon, a vertex on the polygon which will be the anchor point, and when GeoGebra asks the factor by which to dilate, type in the variable name from your slider.
Step 4: Make changes to the polygon and the scaling factor to see how those changes affect your dilated image.

## Construction #5: Composition of Transformations

Below, choose any two of the transformations we made above, and create an applet that does the composition of two transformations.

**Hint: Your second transformation should START with the IMAGE of your first transformation.**Then, write about what you chose to do below.Which two transformations did you choose? How did you make this construction?