Question

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

A) 1/3
B) 1/2
C) 2
D) 3

Answer 1

Answer: B) 1/2

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Step-by-step 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
`\text{black} \to \text{green}`

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.

Answer 2

THE ANSWER IS C)2

Step-by-step explanation:

I GOT IT WRONG CUZ THIS DUDE ABOVE MEEE

(im big mad)