Geometry

Question Analysis

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

Key Concept Explanation

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

Scale factor: Represents 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 extent 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, we find that the center of dilation is .

2. Calculate the scale factor:

Use the distance formula .

For side  with  and :