Use the image to answer the question.

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

1. Left trapezoid side lengths:

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

2. Right trapezoid side lengths:

   • 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 take the ratio of the corresponding sides from the two trapezoids. We'll compare the sides one by one:

• For the base: \[ \text{Scale factor for base} = \frac{\text{Right trapezoid base}}{\text{Left trapezoid base}} = \frac{8}{10} = 0.8 \]

• For the left side: \[ \text{Scale factor for left side} = \frac{\text{Right trapezoid left side}}{\text{Left trapezoid left side}} = \frac{3.2}{4} = 0.8 \]

• For the top: \[ \text{Scale factor for top} = \frac{\text{Right trapezoid top}}{\text{Left trapezoid top}} = \frac{4.8}{4} = 1.2 \]

• For the right side: \[ \text{Scale factor for right side} = \frac{\text{Right trapezoid right side}}{\text{Left trapezoid right side}} = \frac{3.2}{6} \approx 0.5333 \]

Since the scale ratios are not consistent across all corresponding sides, this indicates that the two trapezoids are not similar, and thus no single scale factor applies uniformly across all dimensions.

Based on the two trapezoid dimensions provided, it can be concluded that the overall scaling is not uniform. However, for the dimensions that are consistent, a scale factor of 0.8 can be noted for some sides.

Use the image to answer the 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

0.8
0.8

0.48
0.48

2

To find the scale factor from the left trapezoid to the right trapezoid, we can take the lengths of corresponding sides and calculate the ratios.

1. Left trapezoid side lengths:

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

2. Right trapezoid side lengths:

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

Now we'll calculate the scale factor for each side:

• For the base: \[ \text{Scale factor for base} = \frac{8}{10} = 0.8 \]

• For the left side: \[ \text{Scale factor for left side} = \frac{3.2}{4} = 0.8 \]

• For the top: \[ \text{Scale factor for top} = \frac{4.8}{4} = 1.2 \]

• For the right side: \[ \text{Scale factor for right side} = \frac{3.2}{6} \approx 0.5333 \]

The consistent scale factor for the base and the left side is 0.8. Since we are looking for a single scale factor to describe the transformation from the left trapezoid to the right trapezoid, the scale factor that is used consistently for some of the dimension comparisons is 0.8.

Therefore, the answer is 0.8.