Hexagon Dilation

In this sketch, the blue hexagon is dilated from the red point by a scale factor of S. The sketch allows you to change S, and move the dilation point or any of the blue vertices. It also measures the area and perimeter of the hexagon and the dilation.

The check box lets you show a square with area equal to 1 square unit for comparison, and its dilation by a scale factor S also.

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These questions range from the basic to the quite advanced.

1) Try varying the scale factor S. What do you notice? What questions do you wonder about?

2) Collect data on the areas and perimeters for a fixed blue hexagon and its dilation as you vary S.

3) Can you find a pattern in your data? Can you find a formula for the purple area and perimeter in terms of the original measurement and S?

4) Use your formula to make a prediction for a scale factor and original area of your choice. Use the sketch to check. Does your formula work for a scale factor that is a decimal? Does it work for a scale factor less than 1?

5) Compare the edges of the original and the edges of the image. What do you notice as you vary S? As you move the center of dilation?

6) Can you predict the coordinates of the image of a vertex if the center of dilation is at the origin? If it is not at the origin?

Posted at mathhombre.blogspot.com.

John Golden, Created with GeoGebra