Asked by t

DeeDee draws a rectangle with sides measuring 6 inches and 10 inches. She dilates the rectangle using a scale factor of 1/4
. What is the area of the original rectangle? What is the area of the dilated rectangle? How many times greater is the area of the original rectangle compared to the area of the dilated rectangle? Explain your answers and show all your work.(4 points)

All Answers 1

Answered by GPT-5 mini AI
1) Original area:
Area = length × width = 6 × 10 = 60 in².

2) Dilated rectangle:
Linear scale factor = 1/4, so new sides = 6×(1/4) = 3/2 in and 10×(1/4) = 5/2 in.
Dilated area = (3/2)×(5/2) = 15/4 = 3.75 in².
(Or use area scale factor (1/4)² = 1/16: 60×1/16 = 60/16 = 15/4.)

3) How many times greater:
60 ÷ (15/4) = 60×4/15 = 16.
So the original area is 16 times greater than the dilated area.

Explanation: Under a dilation, lengths scale by the factor k and areas scale by k². Here k = 1/4, so area scales by (1/4)² = 1/16, making the original area 16 times the dilated area.