Geometry

Question Analysis

The main focus is to determine the center of dilation and calculate the scale factor.

Key Concept Explanation

Center of dilation: The fixed point around which a figure is dilated. Lines connecting corresponding points of the pre - image and dilated image intersect at this point.

Scale factor: The ratio of the length of a side in the dilated figure to the length of the corresponding side in the original figure, showing the amount of enlargement or reduction.

Step - by - Step Solution

1. Find the center of dilation:

To find the center of the dilation, you can draw a line through  and  and another line through  and . The intersection point of these two lines is the center of the dilation. In a dilation, all such lines connecting corresponding points will pass through this fixed point, which serves as the center around which the figure is expanded or contracted.

By observing the graph, the intersection point of these lines is .

2. Calculate the scale factor:

Use the distance formula .

For side  with  and :