Final answer:
To find the ratio of side lengths of a new quadrilateral to the corresponding side lengths of the original quadrilateral, set up proportions for the length and width. Solve for the unknown length and width using cross-multiplication. Verify if the calculated ratios are equal to the absolute value of the dilation factor.
Step-by-step explanation:
In this question, we are asked to find the ratio of the side lengths of a new quadrilateral to the corresponding side lengths of the original quadrilateral. We are also asked to verify if these ratios are equal to the absolute value of the dilation factor. To do this, we need to set up proportions for the length and width of the quadrilateral. For example, if the scale factor is 1/10 for length, we can set up the proportion: Length of new quadrilateral / Length of original quadrilateral = 1/10.
Then, we can solve for the unknown length by cross-multiplying: Length of new quadrilateral = Length of original quadrilateral x 1/10. We can do the same for the width of the quadrilateral. Once we have the values for the length and width of the new quadrilateral, we can calculate their ratio to the corresponding side lengths of the original quadrilateral. If these ratios are equal to the absolute value of the dilation factor, then we have verified our answer.