To solve the problem of dilating the figure $ABCDEFGHIJKL$ by a scale factor of $\frac{1}{2}$, you need to reduce each coordinate of the vertices to half its distance from the origin (or the center of dilation if specified).

Steps to Solve the Dilation

1. Identify Coordinates: Locate the coordinates of each vertex $A, B, C, \dots, L$ on the grid.
2. Apply the Scale Factor: Multiply each coordinate by $\frac{1}{2}$. For example:
   • If a vertex is at $(x, y)$, the new coordinates will be $\left( \frac{x}{2}, \frac{y}{2} \right)$.
3. Plot the New Points: Place the new points on the grid and connect them in the same order as the original figure.

Partial Solution Insight

In the image, the segment $K'L'$ has already been plotted after applying the scale factor $\frac{1}{2}$. The other points of the figure need to follow the same procedure.

Would you like a detailed breakdown of each coordinate transformation and step-by-step plotting for this figure?

Related Questions:

1. What are the coordinates of each vertex $A, B, C, \dots, L$ before dilation?
2. How does a dilation with a scale factor of $\frac{1}{2}$ affect the size and position of the figure?
3. How do you graph dilated figures with a center of dilation not at the origin?
4. Can a dilation result in overlapping or congruent images under specific conditions?
5. How do negative scale factors impact dilations on a grid?

Tip:

To ensure accuracy, always start with plotting key vertices first (e.g., $A$ and $B$) and use symmetry or shape consistency for faster construction.