1. **Problem Statement:** We need to identify the transformation that results in a horizontal reflection and a dilation by a scale factor of $\frac{1}{2}$ of an L shape. 2. **Understanding the Transformations:** - A **horizontal reflection** flips the shape over a vertical axis, reversing its left and right sides. - A **dilation** with scale factor $\frac{1}{2}$ reduces the size of the shape to half its original dimensions, centered at a point (usually the origin). 3. **Formula for Dilation:** If a point on the original shape is $(x,y)$, after dilation by scale factor $k=\frac{1}{2}$, the new point is: $$ (x', y') = \left(kx, ky\right) = \left(\frac{x}{2}, \frac{y}{2}\right) $$ 4. **Formula for Horizontal Reflection:** Reflecting horizontally over the y-axis changes $(x,y)$ to: $$ (x', y') = (-x, y) $$ 5. **Combined Transformation:** Applying horizontal reflection first, then dilation: $$ (x,y) \xrightarrow{reflection} (-x,y) \xrightarrow{dilation} \left(-\frac{x}{2}, \frac{y}{2}\right) $$ 6. **Interpretation:** - The pink L shape should be a smaller version (half size) of the blue L shape. - It should be flipped horizontally (mirrored left to right). - The position of the pink L shape should correspond to the coordinates $\left(-\frac{x}{2}, \frac{y}{2}\right)$ of the original points. 7. **Conclusion:** The correct transformation is a horizontal reflection over the y-axis followed by a dilation with scale factor $\frac{1}{2}$, resulting in the pink L shape being half the size and mirrored horizontally relative to the blue L shape. **Final answer:** The transformation is a horizontal reflection combined with a dilation of scale factor $\frac{1}{2}$, mathematically represented as: $$ (x,y) \to \left(-\frac{x}{2}, \frac{y}{2}\right) $$