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, indicating 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 Z and  and another line through Y and . The point where these 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.

The center of dilation is .

2. Calculate the scale factor:

Use the distance formula .

For side with and :

.

For side

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