Question

Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.

Answer 1

Answer:

Options 1,2 and 4 are correct.

Step-by-step explanation:

We have been given a parallelogram MNPQ was dilated to create parallelogram  M'N'P'Q' and we asked to find out which of the given options are correct.

Let us see all the options one by one.

On using distance formula we can see that side MN is 2 units.

$MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }$

$MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }$

$MN=\sqrt{(2)^{2} } =2$

Therefore,option 1 is correct.

We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.

Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.

Now look at our option 4.

Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.

Therefore, option 4 is correct indeed.

Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.

Therefore, our fifth option is false.

Answer 2

Choice A) True. Count out 2 units going from M to N (or vice versa). 
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Choice B) True. Similar reasons as choice A, but this time M' is five units away from N'
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Choice C) False. The pre-image is the original figure MNPQ which enlarges to the image M'N'P'Q'
before -----> after
pre-image ----> image
So the image is larger (not smaller) than the pre-image
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Choice D) True. Use the slope formula m = (y2-y1)/(x2-x1) to compute the slope of each. You'll find both results are 1.
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Choice E) Unknown. This problem is incomplete. It is missing the scale factor. So at this moment it is impossible to answer this portion.
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So in summary, the answers are A, B, and D. The status of choice E is unknown until you provide an update to the problem. 

Update: Choice E is false because 2/5 = 0.4 is smaller than 1, indicating the "after" image is smaller, which is the opposite away around.