1. What is Dilation Scale Factor?

The dilation scale factor is the ratio by which a geometric figure is enlarged or reduced. It's calculated as the ratio of corresponding lengths in the image to the original figure.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• Numerator — Length in the dilated image
• Denominator — Corresponding length in the original figure

Explanation: A scale factor greater than 1 indicates enlargement, less than 1 indicates reduction, and exactly 1 means no size change.

3. Importance of Scale Factor

Details: The scale factor is crucial in geometry, architecture, engineering, and computer graphics for maintaining proportions when resizing objects or drawings.

4. Using the Calculator

Tips: Enter the numerator (image size) and denominator (original size) as positive numbers. The denominator must be greater than zero.

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 (a reduction by 50%).

Q2: What does a scale factor of 2 mean?
A: It means the image is twice as large as the original (an enlargement by 100%).

Q3: Can the scale factor be negative?
A: In this calculator, we consider only positive scale factors. Negative values would indicate reflection in addition to scaling.

Q4: How is scale factor related to area?
A: Area scales by the square of the scale factor. A scale factor of 2 means the area becomes 4 times larger.

Q5: How is scale factor related to volume?
A: Volume scales by the cube of the scale factor. A scale factor of 3 means the volume becomes 27 times larger.