1. What is Scale Factor in Dilation?

The scale factor in dilation describes how much a geometric figure is enlarged or reduced. It's the ratio of corresponding lengths in the image to the original figure.

2. How Does the Calculator Work?

The calculator uses the scale factor formula:

Where:

• Distance_new — Length of corresponding side in the dilated image
• Distance_old — Length of original side before dilation

Explanation: A scale factor >1 indicates enlargement, <1 indicates reduction, and =1 indicates congruent figures.

3. Importance of Scale Factor

Details: Scale factor is crucial in geometry, computer graphics, architecture, and map scaling. It preserves the shape while changing the size of figures.

4. Using the Calculator

Tips: Enter both distances in the same units. The result is dimensionless. Values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a scale factor of 0.5 mean?
A: It means the image is half the size of the original (50% reduction).

Q2: Can scale factor be negative?
A: In pure scaling, no. Negative values typically indicate reflection combined with scaling.

Q3: How is scale factor related to area?
A: Area changes by the square of the scale factor (e.g., scale factor 2 → area ×4).

Q4: What's the difference between scale factor and ratio?
A: Scale factor is specifically the ratio of corresponding lengths in similar figures.

Q5: How does scale factor apply to 3D objects?
A: Volume changes by the cube of the scale factor (e.g., scale factor 3 → volume ×27).