1. What is the Rectangle Scale Factor?

The rectangle scale factor transformation applies independent scaling factors to the x and y coordinates of a rectangle. This operation changes the size of the rectangle while maintaining its shape when scale factors are equal.

2. How Does the Calculator Work?

The calculator uses the scale factor equation:

Where:

• \( x, y \) — Original coordinates
• \( k_x, k_y \) — Scale factors for x and y axes
• \( x', y' \) — Scaled coordinates

Explanation: Each coordinate is multiplied by its corresponding scale factor to produce the new scaled coordinates.

3. Importance of Scaling Coordinates

Details: Coordinate scaling is fundamental in computer graphics, CAD systems, and geometric transformations. It allows for resizing objects while maintaining their relative proportions.

4. Using the Calculator

Tips: Enter original coordinates and desired scale factors. The calculator will compute the new coordinates after scaling.

5. Frequently Asked Questions (FAQ)

Q1: What happens when scale factors are equal?
A: When kₓ = kᵧ, the rectangle scales uniformly, maintaining its original proportions.

Q2: What does a scale factor less than 1 do?
A: A scale factor between 0 and 1 reduces the size of the rectangle in that dimension.

Q3: Can scale factors be negative?
A: Yes, negative scale factors create reflections in addition to scaling.

Q4: How does this relate to area change?
A: The area scales by the product of the scale factors (kₓ × kᵧ).

Q5: What's the difference between scaling and translation?
A: Scaling changes size, while translation moves the object without changing its size or shape.