Question

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

Explanation:

Step1: Understand Dilation Scale Factor

A dilation with a scale factor between 0 and 1 creates a smaller image. The closer the scale factor is to 0, the smaller the image. So, we compare the sizes of the dilated (green) quadrilaterals relative to the original (blue) one.

Step2: Analyze Each Dilation

• Dilation B: The green quadrilateral is the smallest among the three dilations. So it should match the smallest scale factor, \( \frac{1}{4} \) (option 1).
• Dilation A: The green quadrilateral is the largest among the three dilations (closest to the original size). So it should match the largest scale factor here, \( \frac{3}{4} \) (option 3).
• Dilation C: The green quadrilateral is of medium size, so it matches the middle scale factor, \( \frac{1}{2} \) (option 2).

Answer:

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