A triangle has an area of 100 square inches. It’s dilated by a factor of .

Mai says, “The dilated triangle’s area is 25 square inches.”

Lin says, “The dilated triangle’s area is 6.25 square inches.”

1. For each student, decide whether you agree with their student's statement. If you agree, explain why. If you disagree, explain what the student may have done to arrive at their answer.
2. Calculate the area of the image if the original triangle is dilated by each of these scale factors:

1. Suppose the artist has enough primer to cover 1 square foot, and she buys another bottle. 
   1. What is the scale factor for a 1 square foot painting?
   2. What is the scale factor for the 11 square foot painting?
   3. Find the rate of change between the original amount of paint and the new total.
2. Suppose the artist has enough primer to cover 16 square feet, and she buys another bottle. Find the rate of change between the original amount of paint and the new total.
3. The artist also needs to stretch the canvas onto a frame. The original painting had a perimeter of 4 feet. The function representing the scale factor for a given length of frame, is . Graph the function. Verify that the graph gives the correct scale factors for a perimeter of 4 feet and a perimeter of 8 feet.

4. Compare the graph of square feet vs. scale factor to the graph of perimeter vs. scale factor.