An illustration shows two parallelograms positioned in different ways. One shows the longer side along the base, and the other is tilted upward to the left, with a longer vertical side. The first parallelogram shows one parallel side as 5 inches and the adjacent side as 3.5 inches. The second parallelogram shows one parallel side as 0.7 inches and the adjacent vertical side as 1 inch.

Question

Kamla draws the parallelogram on the left and then uses a scale factor to create the parallelogram on the right. All measurements are in inches. What scale factor does he use?

(1 point)
Responses

5
5

4
4

3.5
3.5

0.2

Answer 1

To find the scale factor between the two parallelograms, we can compare the corresponding sides.

For the first parallelogram:

• One side (base) = 5 inches
• Adjacent side = 3.5 inches

For the second parallelogram:

• One side (base) = 0.7 inches
• Adjacent side (vertical) = 1 inch

Let's calculate the scale factors for the corresponding sides:

1. For the base: $$\text{Scale factor}=\frac{\text{Base of the second parallelogram}}{\text{Base of the first parallelogram}}=\frac{0.7}{5}=0.14$$

2. For the adjacent side: $$\text{Scale factor}=\frac{\text{Adjacent side of the second parallelogram}}{\text{Adjacent side of the first parallelogram}}=\frac{1}{3.5}\approx 0.2857$$

Since the scale factors for both corresponding sides should be the same for the transformation from the first parallelogram to the second parallelogram, we look for a common factor.

Since neither of these calculations yields a clear integer, it suggests that the scale factor is not a whole number. However, if we examine the relationships:

If we double-check the scale factor based purely on the first parallelogram's base and the second parallelogram's adjacent vertical side measurements:

0.7 inches corresponds to 5 inches when viewed proportionally, suggesting:

If we take 5 times the scale factor to find what results in 0.7: $$\text{Scale factor}=\frac{0.7}{5}\approx 0.14$$

This is not what the possible answers are. In fact, using 0.2 (1/5) for a more refined calculation. Given that the factor can relate to a scaling ratio between base and height:

As such, the closest response option here remains the answer selection:

• 0.2

Thus, the correct answer is 0.2.