Answer: B) 1/2
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Explanation:
"The green parallelogram is a dilation of the black parallelogram"
This tells us that the preimage is the black parallelogram and the image is the green one.
In short, the mapping is [tex]\text{black} \to \text{green}[/tex]
The image is smaller than the preimage (green is smaller than black), indicating the scale factor is some value of k such that 0 < k < 1. We can rule out choices C and D because of this.
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Measuring along the top, we can see that the black parallelogram goes from x = -6 to x = 8. Check out the image shown below where I've marked your given diagram, adding on helpful lines to show this going on.
The number-line distance from x = -6 to x = 8 is 14 units, so the top side of the black parallelogram is 14 units long.
The corresponding top side of the green parallelogram is 7 units long (because it spans from x = -3 and x = 4; as shown in blue in the figure below).
Divide the image length over its corresponding preimage length to get the scale factor.
scale factor = (image length)/(preimage length)
scale factor = 7/14
scale factor = 1/2
which points to choice B as our final answer.
