1. What is Dilation with Scale Factor?

Dilation is a transformation that changes the size of an object by a scale factor while maintaining its shape. The scale factor determines whether the object is enlarged (k > 1), reduced (0 < k < 1), or remains the same size (k = 1).

2. How Does the Calculator Work?

The calculator uses the dilation formula:

Where:

• \( \text{new\_size} \) — The size after dilation (units)
• \( \text{old\_size} \) — The original size before dilation (units)
• \( k \) — The scale factor (unitless)

Explanation: The formula multiplies the original size by the scale factor to determine the new size after dilation.

3. Importance of Scale Factor

Details: Scale factor is crucial in geometry, computer graphics, architecture, and engineering for resizing objects while maintaining proportions. It's used in map scaling, image resizing, and 3D modeling.

4. Using the Calculator

Tips: Enter the original size in any units and the scale factor. The result will be in the same units as the original size. Positive scale factors maintain orientation, while negative scale factors create reflections.

5. Frequently Asked Questions (FAQ)

Q1: What does a scale factor of 2 mean?
A: A scale factor of 2 means the object will be twice as large in all dimensions.

Q2: What happens with a scale factor between 0 and 1?
A: The object becomes smaller (a reduction) while maintaining its proportions.

Q3: What does a negative scale factor do?
A: A negative scale factor both resizes the object and reflects it across the origin or center point.

Q4: How does this relate to area and volume scaling?
A: For area, multiply by k². For volume, multiply by k³. This calculator handles linear dimensions only.

Q5: Can I use this for 2D or 3D objects?
A: Yes, but you'll need to apply it to each dimension separately or use it with coordinate points.