1. What is Dilation Scale?

Dilation scale (k) is a transformation that changes the size of a figure without changing its shape. It's a fundamental concept in geometry and graphics that uniformly stretches or shrinks objects.

2. How Does the Calculator Work?

The calculator uses the dilation formula:

Where:

• \( k \) — Scale factor (unitless)
• If original measurement is provided: \( \text{Dilated} = \text{Original} \times k \)

Explanation: A scale factor >1 enlarges the figure, between 0 and 1 shrinks it, and negative values create a reflection plus scaling.

3. Importance of Scale Factor

Details: Scale factors are crucial in map making, architectural design, computer graphics, and scientific modeling to represent objects at different sizes while maintaining proportions.

4. Using the Calculator

Tips: Enter the scale factor (k). Optionally enter an original measurement to calculate its dilated size. Positive values scale, negative values scale and reflect.

5. Frequently Asked Questions (FAQ)

Q1: What does a scale factor of 0.5 mean?
A: It means the figure will be reduced to half its original size in all dimensions.

Q2: What happens with negative scale factors?
A: Negative values create a reflection (inversion) plus scaling. A scale of -1 is a pure reflection.

Q3: How does dilation differ from rotation or translation?
A: Dilation changes size only, while rotation turns the figure and translation moves it without changing size or orientation.

Q4: Can scale factors be different for x and y dimensions?
A: This calculator assumes uniform scaling. Non-uniform scaling (different x/y factors) would stretch the figure disproportionately.

Q5: How is dilation used in real-world applications?
A: Used in photography (zoom), map scaling, CAD designs, 3D modeling, and scientific visualizations of microscopic/astronomical objects.