Dilating Area

A rectangle with area 12 square units is dilated by a scale factor of $$k$$ . Find the area of the image for each given value of $$k$$ . $$k=\frac14$$

A rectangle with area 12 square units is dilated by a scale factor of $$k$$ . Find the area of the image for each given value of $$k$$ . $$k=1.2$$

Trapezoid $$A’B’C’D$$ was created by dilating trapezoid $$ABCD$$ using $$D$$ as the center of dilation. Description: A large trapezoid A'B'C'D' comprised of smaller shapes on a grid. The blue shape ABCD is a smaller trapezoid. Triangle Q in top right corner. Quadrilateral P in lower right corner. What was the scale factor of the dilation?

Trapezoid $$A’B’C’D$$ was created by dilating trapezoid $$ABCD$$ using $$D$$ as the center of dilation. Description: A large trapezoid A'B'C'D' comprised of smaller shapes on a grid. The blue shape ABCD is a smaller trapezoid. Triangle Q in top right corner. Quadrilateral P in lower right corner. How can you see your answer to these questions in the diagram?

Select the solid whose cross sections are dilations of some two-dimensional shape using a point directly above the shape as a center and scale factors ranging from 0 to 1.

Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above the plane and a scale factor between 0 and 1. Estimate the scale factor that was used for each dilation. Dilation C.

Each solid in the image has height 4 units. The area of each solid’s base is 8 square units. A cross section has been created in each by dilating the base using the apex as a center with scale factor $$k=0.25$$ . Calculate the area of each of the 2 cross sections.

Suppose a new cross section was created in each solid, both at the same height, using some scale factor $$k$$ . How would the areas of these 2 cross sections compare? Explain your reasoning.

A trapezoid has an area of 10 square units. What scale factor would be required to dilate the trapezoid to have an area of 90 square units?

When ​ (a)   a figure, you will always ​ (b)   by a ​ (c)   factor.