1. What is Dilation?

Dilation is a transformation that changes the size of a figure by a scale factor while maintaining its shape. It can result in either an enlargement (scale factor > 1) or reduction (0 < scale factor < 1).

2. How Does the Calculator Work?

The calculator uses the dilation formula:

Where:

• \( \text{scale} \) — Scale factor (unitless)
• \( \text{distance}_{\text{new}} \) — Distance after dilation
• \( \text{distance}_{\text{original}} \) — Original distance before dilation

Explanation: The scale factor is calculated by dividing the new distance by the original distance. This ratio determines how much the figure has been enlarged or reduced.

3. Importance of Dilation Calculation

Details: Calculating dilation is essential in geometry, computer graphics, architecture, and engineering for scaling objects while maintaining proportions.

4. Using the Calculator

Tips: Enter both distances in the same units. The scale factor will be unitless. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a scale factor of 1 mean?
A: A scale factor of 1 means the figure remains unchanged - the new distance equals the original distance.

Q2: What's the difference between positive and negative scale factors?
A: Positive scale factors maintain orientation, while negative scale factors create a reflection in addition to the size change.

Q3: How does dilation relate to similar figures?
A: Dilation produces similar figures - they have the same shape but different sizes, with corresponding sides proportional.

Q4: Can the scale factor be zero?
A: Mathematically yes, but geometrically a scale factor of zero would collapse the figure to a single point.

Q5: How is dilation used in real-world applications?
A: Dilation is used in photography (zoom), map scaling, architectural blueprints, and computer graphics rendering.