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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

0.48
0.48

1.25
1.25

0.8
0.8

2

Answer 1

To determine the scale factor from the first trapezoid to the second trapezoid, we need to compare corresponding lengths of the sides of the trapezoids.

Dimensions of the First Trapezoid:

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

Dimensions of the Second Trapezoid:

• Base: 8 cm (slanted base)
• Left Side: 3.2 cm
• Top Side: 4.8 cm
• Right Side: 3.2 cm

Next, we will calculate the scale factor by comparing the lengths of the corresponding sides:

1. Base:

   • 8 cm (second trapezoid) / 10 cm (first trapezoid) = 0.8

2. Left Side:

   • 3.2 cm (second trapezoid) / 4 cm (first trapezoid) = 0.8

3. Top Side:

   • 4.8 cm (second trapezoid) / 4 cm (first trapezoid) = 1.2

4. Right Side:

   • 3.2 cm (second trapezoid) / 6 cm (first trapezoid) = 0.5333 (approximately)

From these calculations, the scale factor appears consistent for the base and left side but varies for the top and right side. However, since we are looking for a common scale factor based on the sides where it is consistent, we observe that the base and left side have a scale factor of 0.8.

Thus, the scale factor that Rashaan uses to create the trapezoid on the right from the one on the left is:

0.8