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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

3.5
3.5

4
4

0.2
0.2

5

1 answer

To find the scale factor used to resize the first parallelogram into the second one, we need to compare the corresponding sides of the two parallelograms.

From the first parallelogram, we have:

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

From the second parallelogram, we have:

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

To find the scale factor from the first to the second parallelogram for the corresponding sides:

For the side that is 5 inches in the first parallelogram: Scale factor = second parallelogram side / first parallelogram side = 0.7 inches / 5 inches = 0.14.

For the side that is 3.5 inches in the first parallelogram: Scale factor = second parallelogram side / first parallelogram side = 1 inch / 3.5 inches = approximately 0.2857.

Since the scale factors are not constant (0.14 and 0.2857), it indicates that the figure was not scaled down uniformly in both dimensions. However, if we’re looking for one of the provided options based solely on the side measurements:

  • The scale factor that most closely relates to these side measurements and represents a decrease would be 0.2.

So, the correct response is: 0.2.