Each layer of the pyramid is a dilation. The point of dilation is the vertex, point E. When the scale factor is 1, the dilation (cross section GHIJ, or polygon 2) is the same as the base (ABCD or polygon 1). With the base length AB = 4, the scale factor will be a ratio: k = HG/AB. Make a table with the following values: AB = 4 Area poly1 = 16 k HG Area poly2 .25 ____ _____ .5 ____ _____ .75 ____ _____ 1 ____ _____
Repeat this using a different base length (such as AB = 6, or AB = 8 or AB = 10). Again, record AB = ___, Area poly1 = ___, and make the table.
Staying in 3 dimensions, what would a dilation by the scale factor k = 0 look like? Where would it be located in the pyramid?
How was the area affected with changes to the cross section? Specifically, was the area of the dilated rectangle also changed by a factor of k?
Is dilating a square using a factor of 0.9, then dilating the image using a scale factor of 0.9 the same as dilating the original square using a factor of 0.8? Explain and show your reasoning.