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

2
2

0.8
0.8

0.48

Answer 1

To find the scale factor between the two trapezoids, we need to compare the corresponding sides of each trapezoid.

From the first trapezoid (left):

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

From the second trapezoid (right):

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

To find the scale factor, we can divide the dimensions of the second trapezoid by the corresponding dimensions of the first trapezoid (where applicable).

Let's take the base: Scale factor from base = \( \frac{8 \text{ cm}}{10 \text{ cm}} = 0.8 \)

Now let's verify this scale factor with the other sides:

1. Left side: \( \frac{3.2 \text{ cm}}{4 \text{ cm}} = 0.8 \)
2. Top: \( \frac{4.8 \text{ cm}}{4 \text{ cm}} = 1.2 \) (this one does not match, indicating a different shape)
3. Right side: \( \frac{3.2 \text{ cm}}{6 \text{ cm}} \approx 0.53 \) (this one also does not match)

Since the left and base sides consistently yield a scale factor of 0.8, that is the likely scale factor used to go from the first trapezoid to the second for those dimensions.

Thus, the correct answer is:

0.8