Dilating a Shape From a Center
A dilation changes the size of a figure using a center and a scale factor. Every point of the original shape moves along the line that connects it to the center. The new point stays on the same line, and its distance from the center is multiplied by the scale factor.
Method
- Identify the center of dilation and the scale factor.
- For each vertex, draw or imagine the line from the center through that vertex.
- Multiply the distance from the center to the vertex by the scale factor.
- Place the new point on the same line at the new distance.
- Repeat for all vertices, then connect the image points in order.
Useful checks
- The image should keep the same shape as the original.
- Corresponding sides should be parallel.
- Distances from the center should all be scaled by the same factor.
- If the scale factor is greater than 1, the figure grows; if it is between 0 and 1, the figure shrinks.
Final check
Make sure the new figure is positioned correctly relative to the center and that your answer is simplified if coordinates or fractions appear.