Question

The black trapezoid is a dilation of the green trapezoid. What is the scale factor of the dilation?

Answer 1

The dilation is by 1/5

Answer 2

Answer: Choice A)  1/5

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Explanation:

We're told that "The black trapezoid is a dilation of the green trapezoid". This means the black trapezoid is the image, while the green one is the preimage. In other words, the green is the "before" and the black is the "after". The mapping is $\text{green} \to \text{black}$ because of the ordering $\text{preimage} \to \text{image}$

Since the green figure (preimage) is larger than the black figure (image), the scale factor must be some value k such that 0 < k < 1. That narrows the answer choices between A and B.

Focus on the green trapezoid. The bottom left corner is at (-10,0). The bottom right corner is at (5,0). The distance between these two points is 15 units.

Using the same idea, the distance along the bottom edge of the black trapezoid is 3 units. We can count out the spaces along the bottom, or we can note the two bottom corners are at (-2,0) and (1,0).

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So far we found:

• The bottom edge of the green trapezoid is 15 units
• The bottom edge of the black trapezoid is 3 units

These two edges correspond to one another. We divide the values to get the scale factor. We divide the image length over its corresponding preimage length.

scale factor = (image length)/(preimage length)

scale factor = 3/15

scale factor = 1/5