Enlargement vs. Reduction: Understanding Scale in Dilations

📚 Understanding Enlargement and Reduction in Dilations

Dilation is a transformation that changes the size of a figure. It can either make the figure bigger (enlargement) or smaller (reduction). The scale factor determines whether the dilation is an enlargement or a reduction.

🔎 Definition of Enlargement

An enlargement occurs when the scale factor is greater than 1. This means every length in the original figure (pre-image) is multiplied by a number greater than 1, resulting in a larger figure (image).

📉 Definition of Reduction

A reduction occurs when the scale factor is between 0 and 1 (exclusive). This means every length in the original figure is multiplied by a number between 0 and 1, resulting in a smaller figure.

Comparison Table: Enlargement vs. Reduction

Feature	Enlargement	Reduction
Scale Factor (k)	$k > 1$	$0 < k < 1$
Size of Image	Larger than pre-image	Smaller than pre-image
Effect on Lengths	Lengths are multiplied by a factor greater than 1	Lengths are multiplied by a factor between 0 and 1
Example	Scale factor of 2	Scale factor of 0.5

💡 Key Takeaways

• 📏 Scale Factor: The scale factor is the key to determining whether a dilation is an enlargement or a reduction.
• 📈 Enlargement: If the scale factor is greater than 1, the figure gets bigger.
• 📉 Reduction: If the scale factor is between 0 and 1, the figure gets smaller.
• 📐 Similarity: Dilations produce similar figures, meaning the angles remain the same, but the side lengths change proportionally.
• ➗ Calculations: To find the new side length after dilation, multiply the original side length by the scale factor.