A parallelogram has an area of 10 square feet.

1. Complete the table that shows the relationship between the dilated area (\(x\)) and the scale factor (\(y\)).

   dilated area in square feet	scale factor
   0
   40
   160
   360
   640

2. Plot the points in the table on coordinate axes, and connect them to create a smooth curve.

A figure has an area of 4 square units. The equation \(y=\sqrt{\frac{x}{4}}\) represents the scale factor of \(y\) by which the solid must be dilated to obtain an image with area \(x\) square units. Select all points that are on the graph representing this equation.

Tyler is designing a banner that will welcome people to a festival. The design for the banner has an area of 1.5 square feet. The actual banner will be a dilation of the design by a factor of 5. What will the area of the actual banner be?

The horizontal cross-sections of this figure are dilations of the bottom rectangle using a point above the rectangle as a center and scale factors from \(\frac12\) to 1. Sketch an example of a cross-section that is created from using a scale factor of \(\frac34\). Label the dimensions of the cross-section that you sketch.

Two distinct lines, \(\ell\) and \(m\), are each perpendicular to the same line \(n\).  Explain why \(\ell\) and \(m\) are parallel lines.