1. What Are Rectangular Scale Factors?

Scale factors (k_x and k_y) describe how much a rectangle has been stretched or compressed in the horizontal and vertical directions during a transformation. They are the ratios of the new dimensions to the original dimensions.

2. How Does the Calculator Work?

The calculator uses these simple formulas:

Where:

• \( k_x \) — Horizontal scale factor (unitless)
• \( k_y \) — Vertical scale factor (unitless)
• \( \text{new\_width} \) — Width after transformation
• \( \text{old\_width} \) — Original width
• \( \text{new\_height} \) — Height after transformation
• \( \text{old\_height} \) — Original height

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

3. Applications of Scale Factors

Details: Scale factors are used in computer graphics, engineering drawings, architecture, and any field where objects need to be proportionally resized while maintaining their aspect ratio.

4. Using the Calculator

Tips: Enter all dimensions in the same units. The calculator works with any unit system (mm, cm, inches, etc.) as long as all inputs use the same units.

5. Frequently Asked Questions (FAQ)

Q1: What if the scale factors are different in x and y directions?
A: Different scale factors create a non-uniform scaling, which will distort the original shape (stretching or squashing it).

Q2: What does a negative scale factor mean?
A: A negative scale factor indicates reflection (mirror image) along that axis in addition to scaling.

Q3: How is this related to aspect ratio?
A: If k_x = k_y, the aspect ratio is preserved. If they differ, the aspect ratio changes.

Q4: Can I use this for 3D objects?
A: For 3D, you would need a third scale factor (k_z) for depth scaling.

Q5: What's the difference between scale factor and multiplication factor?
A: They are essentially the same concept - both represent how much a dimension has been multiplied by in a transformation.