Dilation with Scale Factor

The scale factor determines the amount of enlargement or reduction in a dilation. It is a ratio comparing the corresponding lengths of the pre-image and image. A scale factor greater than 1 indicates enlargement, while a factor between 0 and 1 implies reduction.

How to Calculate Scale Factor in Dilation?

To calculate the scale factor in dilation, divide the length of a corresponding side in the image by its corresponding side in the pre-image. This provides insight into the proportional relationship and helps understand the extent of the dilation.

Below are the steps to Calculate the Scale Factor in Dilation:

• The scale factor (h) can be found by comparing corresponding lengths in the original and dilated figures.

h = {length in dilated figure}/ length in dilated figure

Example: If AB in the original triangle is 6 units and AB’ in the dilated triangle is 12 units find the scale factor.

Solution:

Given,

• Original Height = 6
• Dilated Height = 12

h = Dilated Height/Original Height = 12/6 = 2

Dilation a transformative process in geometry involves resizing a figure while maintaining its shape around a fixed center point. The essence of dilation lies in its ability to expand or contract geometric shapes providing a versatile tool for mathematical analysis. Dilation in Geometry is a geometric operation that introduces the concept of a scale factor determining the degree of enlargement or reduction applied to a figure.

Exploring dilation helps in establishing similarity between figures which is a key aspect in geometry and real-world applications. When a figure undergoes dilation, all its points move radially from or towards the fixed center emphasizing the directional nature of this transformation. In practical terms, dilation finds relevance in fields like cartography where maps undergo scaling to represent different geographical areas accurately.