Short Answer 
To perform a dilation, first identify the center of dilation, which serves as the reference for measuring distances. Next, calculate the new image points by applying the specified dilation ratio, ensuring that each point is positioned twice as far from the center as before. Finally, verify the accuracy of all calculated points to confirm the dilation process has been correctly executed.
Step 1: Understanding the Center of Dilation
The first crucial element in solving this problem is to identify the center of dilation. This will be the reference point from which all distances are measured. The dilation involves moving each vertex of the shape away from this center by a specified ratio. In this case, every vertex will move twice as far from the center as it is in the original shape.
Step 2: Calculating Image Points
Next, calculate the new image points based on the distances from the center of dilation. For example, if a vertex is 2 units left from the center in the pre-image, the corresponding image point will be 4 units left (2 * 2) from the center. Use the formula to determine the coordinates of each image point and ensure they maintain the same direction relative to the center of dilation.
- Original point: (-5, 2) – Move 3 left and 4 up.
- New image point: (-8, 6) – Move 6 left and 8 up from the center.
Step 3: Verify and Finalize the Points
Lastly, once all the image points are calculated, verify their accuracy by checking their distances from the center of dilation. Ensure that each image point is indeed located twice as far as its corresponding pre-image point. This is essential for confirming that the dilation has been executed correctly and the transformation adheres to the defined ratio.