1. What is the Scale Factor Formula?

The scale factor formula calculates new coordinates after applying a scaling transformation. It's used in geometry, computer graphics, and engineering to resize objects while maintaining their proportions.

2. How Does the Calculator Work?

The calculator uses the scale factor formula:

Where:

• \( x, y \) — Original coordinates (length units)
• \( x', y' \) — Scaled coordinates (length units)
• \( k \) — Scale factor (unitless)

Explanation: Each coordinate is multiplied by the scale factor to produce the new scaled coordinates. A scale factor >1 enlarges, <1 reduces, and =1 maintains the same size.

3. Importance of Coordinate Scaling

Details: Coordinate scaling is fundamental in computer graphics, CAD systems, map making, and any application where objects need to be resized proportionally.

4. Using the Calculator

Tips: Enter original coordinates in any consistent units, and the scale factor (positive values). The calculator will output the new coordinates in the same units.

5. Frequently Asked Questions (FAQ)

Q1: What happens with negative scale factors?
A: Negative scale factors create a reflection (inversion) in addition to scaling. The absolute value determines the size change.

Q2: Can I scale 3D coordinates with this?
A: The same principle applies to 3D coordinates: (x', y', z') = (k*x, k*y, k*z).

Q3: How does this relate to vector scaling?
A: This is exactly vector scaling - multiplying a vector (x,y) by a scalar k.

Q4: What about non-uniform scaling?
A: For different scaling in x and y directions, use different scale factors: (k₁*x, k₂*y).

Q5: How is this used in computer graphics?
A: This is part of transformation matrices used to scale objects in 2D and 3D graphics.