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, which indicates the amount of enlargement or reduction.

Step - by - Step Solution

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 point where these two lines intersect is the center of the dilation. In a dilation, all such lines connecting corresponding points will pass through this fixed point, which is the center around which the figure is expanded or contracted.

By observing the graph, the intersection point is .

2. Calculate the scale factor:

Use the distance formula .

For side with and :

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