Final answer:
To find the scale factor of a dilation from figure P to similar figure Q, compare the corresponding lengths. The scale factor of 1:4 means each unit of P corresponds to 4 units of Q. By setting up proportions, you can solve for missing dimensions and remember that the area ratio is the square of the scale factor.
Step-by-step explanation:
To determine the scale factor of the dilation that takes figure P to figure Q, you need to compare the corresponding lengths of the two similar quadrilaterals. If you have a scale dimension for a smaller figure, you can use the proportion to find the actual dimension for the larger figure. For example, if the scale factor is given as 1:4, this means for every 1 unit of measurement on figure P, there are 4 of the same units of measurement on figure Q.
Let's consider a specific example where the scale dimension is given as 4 units. Using the proportion 1:2 = 4:x, where x represents the actual dimension in the larger figure, we can solve for x by setting up a cross-multiplication:
1 * x = 2 * 4
x = 8
Furthermore, when we compare the areas of the two similar figures, the ratio of their areas is the square of the scale factor. If we know that figure Q has an area 4 times larger than figure P, then the scale factor when comparing their sides would be the square root of 4, which is 2. This means that every side of figure Q is 2 times longer than the corresponding sides of figure P.