Use the image to answer the question.

Question

An illustration shows two trapezoids positioned in different ways. The first is straight on the baseline; the second is tilted upward to the left. The sides of the first trapezoid are 10 centimeters along the base, 4 centimeters on the left side, 4 centimeters along the top side, and 6 centimeters on the right side. The sides of the second trapezoid are 8 centimeters along the slanted base, 3.2 centimeters, 3.2 centimeters, 4.8 centimeters.

Rashaan draws these two trapezoids with the dimensions labeled in centimeters. What scale factor does he use to create the trapezoid on the right from the one on the left?

(1 point)
Responses

1.25
1.25

0.48
0.48

0.8
0.8

2

Answer 1

To find the scale factor used to create the trapezoid on the right from the trapezoid on the left, we need to compare the lengths of corresponding sides of the two trapezoids.

The trapezoid on the left has the following dimensions:

• Base: 10 cm
• Left side: 4 cm
• Top side: 4 cm
• Right side: 6 cm

The trapezoid on the right has the following dimensions:

• Slanted base: 8 cm
• Left side: 3.2 cm
• Top side: 4.8 cm
• Right side: 3.2 cm

We can calculate the scale factor using the lengths of corresponding sides:

1. For the bases:

   • Left trapezoid base: 10 cm
   • Right trapezoid base: 8 cm
   • Scale factor for the base = \( \frac{8}{10} = 0.8 \)

2. For the left and right side:

   • Left trapezoid left side: 4 cm
   • Right trapezoid left side: 3.2 cm
   • Scale factor for the left side = \( \frac{3.2}{4} = 0.8 \)

3. For the top side:

   • Left trapezoid top side: 4 cm
   • Right trapezoid top side: 4.8 cm
   • Scale factor for the top side = \( \frac{4.8}{4} = 1.2 \)

4. For the right side:

   • Left trapezoid right side: 6 cm
   • Right trapezoid right side: 3.2 cm
   • Scale factor for the right side = \( \frac{3.2}{6} \approx 0.53 \)

From the measurements, we see that the scale factor used is not consistent among all sides. However, focusing on the base and most of the sides (except for the top), consistently gives us a scale factor of 0.8.

Thus, Rashaan uses a scale factor of 0.8 to create the trapezoid on the right from the one on the left.

So, the answer is: 0.8