1. **State the problem:** We have a pre-image with points B(8,4), U(6,10), N(5,-2) and an image with points B'(2,1), U'(1.5,2.5), N'(1.25,-0.5). We need to find the transformation rule $(x,y) \to (x',y')$ that maps the pre-image to the image. 2. **Identify the transformation type:** The image points appear to be scaled versions of the pre-image points. We check the scale factors for x and y coordinates. 3. **Calculate scale factors:** - For point B: $x$ scale factor = \frac{2}{8} = 0.25\), $y$ scale factor = \frac{1}{4} = 0.25\) - For point U: $x$ scale factor = \frac{1.5}{6} = 0.25\), $y$ scale factor = \frac{2.5}{10} = 0.25\) - For point N: $x$ scale factor = \frac{1.25}{5} = 0.25\), $y$ scale factor = \frac{-0.5}{-2} = 0.25\) 4. **Confirm uniform scaling:** Since both $x$ and $y$ coordinates are multiplied by 0.25, the transformation is a dilation with scale factor 0.25. 5. **Write the transformation rule:** $$ (x,y) \to (0.25x, 0.25y) $$ 6. **Explanation:** This means every point $(x,y)$ in the pre-image is scaled down by a factor of 4 (since 0.25 = \frac{1}{4}) in both the x and y directions to get the image point $(x',y')$.