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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.

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

0.2
0.2

3.5
3.5

4
4
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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To find the scale factor used to create the second parallelogram from the first, we compare corresponding sides of the two parallelograms.

For the first parallelogram:

  • One side = 5 inches
  • Adjacent side = 3.5 inches

For the second parallelogram:

  • Corresponding side = 0.7 inches
  • Corresponding vertical side = 1 inch

Now, we calculate the scale factor for both dimensions:

  1. From the longer side: \[ \text{Scale factor} = \frac{\text{First parallelogram side}}{\text{Second parallelogram side}} = \frac{5}{0.7} \approx 7.14 \]

  2. From the shorter adjacent side: \[ \text{Scale factor} = \frac{3.5}{1} = 3.5 \]

The second parallelogram is scaled down from the first parallelogram, and therefore the appropriate scale factor can be calculated from these measurements. The calculations, however, indicate that the simpler approach is using a consistent comparison.

To find the overall consistent scale factor from the first side to second side corresponding dimensions (since it should ideally be the same for the geometric consistency):

We check the most relevant comparison which appears to closely align, for calculation consistency of \(0.2\) we would check \(5 \times 0.2 = 1\) and similarly \(3.5 \times 0.2 = 0.7\).

Thus the scale factor that Kamla uses to create the parallelogram on the right from that on the left is:

0.2