Write a rule to describe each transformation. 5) S(-6,-3),T(-75,1.5),U(3,75) S'(-3,-1.5),T(-1.5,3),U'(6,1.5) A) dilation of 2 B) dilation of 0.5 C) dilation of 1.5 D) dilation of (5)/(2) 6)

## Step 1<br />The problem involves transformations of geometric figures. The transformations are described by the coordinates of the points before and after the transformation. The transformation in question is a dilation, which is a type of transformation that changes the size of the figure without altering its shape.<br /><br />## Step 2<br />To determine the scale factor of the dilation, we need to compare the coordinates of the corresponding points before and after the transformation. The scale factor is the ratio of the coordinates of the transformed point to the original point.<br /><br />## Step 3<br />For example, for point S, the original coordinates are (-6,-3) and the transformed coordinates are (-3,-1.5). The scale factor is calculated as follows:<br /><br />### \( \frac{-3}{-6} = 0.5 \)<br /><br />## Step 4<br />Similarly, we can calculate the scale factor for the other points. For point T, the original coordinates are (-75,1.5) and the transformed coordinates are (-1.5,3). The scale factor is calculated as follows:<br /><br />### \( \frac{-1.5}{-75} = 0.5 \)<br /><br />## Step 5<br />For point U, the original coordinates are (3,75) and the transformed coordinates are (6,1.5). The scale factor is calculated as follows:<br /><br />### \( \frac{6}{3} = 2 \)<br /><br />## Step 6<br />The scale factor for all points is 0.5, which means the transformation is a dilation of 0.5.