Question

geometry – unit 5 – lessons 3 - 4 practice problems name:______

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. match the dilation with the scale factor used.

dilation a dilation b dilation c
a. dilation a 1. \\(\frac{1}{4}\\)
b. dilation b 2. \\(\frac{1}{2}\\)
c. dilation c 3. \\(\frac{3}{4}\\)

Explanation:

Step1: Recall Dilation Concept

Dilation with scale factor \( k \) (0 < \( k \) < 1) shrinks the figure. Smaller scale factor means more shrinkage.

Step2: Analyze Each Dilation

• Dilation B: The image is the smallest (most shrunk), so scale factor \( \frac{1}{4} \) (1).
• Dilation A: The image is the largest among the shrunk ones (least shrinkage), so scale factor \( \frac{3}{4} \) (3).
• Dilation C: The image size is between B and A, so scale factor \( \frac{1}{2} \) (2).

Step3: Match

• Dilation A (\( \frac{3}{4} \)): A - 3
• Dilation B (\( \frac{1}{4} \)): B - 1
• Dilation C (\( \frac{1}{2} \)): C - 2

Answer:

A. Dilation A - 3
B. Dilation B - 1
C. Dilation C - 2