Dilate quadrilateral ABCD with the origin as the center of dilation and a scale factor of 2.5. Record the side lengths of the corresponding sides in each quadrilateral. Round your answers to the hundredths place. Verify that the ratio of each side length of A′B′C′D′ to the corresponding side length of ABCD is equal to the dilation factor.

Step-by-step explanation:

Dilation about the origin is accomplished by multiplying each coordinate by the dilation factor.

Using GeoGebra, the dilation by a factor of 2.5 is easily accomplished by defining the dilated points as ...

  A' = 2.5A

  B' = 2.5B

  C' = 2.5C

  D' = 2.5D

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GeoGebra can be set to display the lengths of the line segments, so we have done that in the first attachment. They are computed as the root of the sum of the squares of the differences in x- and y-coordinates. That computation is programmed into the spreadsheet of the second attachment.

The second attachment lists the dilated coordinates and the lengths computed for each of the segments.

The RATIO calculation divides the dilated segment length by the original segment length. It verifies that all segments in the dilated figure are 2.5 times the corresponding length in the pre-image.

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Segment lengths are calculated using the distance formula:

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Comment on coordinates

We have used the coordinates shown in the problem statement for the given points. However, we note that the quadrilateral areas reported are different for the given problem and our attempt to copy it. (4.54 vs 4.55) This suggests that one or more point coordinates are actually slightly different from the value shown in the problem. Of course, that difference would have to be in the hidden 3rd decimal place.

nada

step-by-step explanation:

x = 23.78

step-by-step explanation: