Geometric Scaling Tool

Visualize how geometric objects are scaled by a factor from a center point. Enter your object's coordinates, scaling center, and factor to see the transformation instantly.

Input Parameters

Enter the coordinates of your geometric object, the scaling center, and the scale factor. Coordinates should be comma-separated (e.g., x1, y1, x2, y2,...).

Object Coordinates

Example: x1, y1, x2, y2, ... for polygon vertices

Scaling Center

Example: x, y coordinates of the center point

Scale Factor

Factor by which the object will be scaled

Scaled Object Coordinates

Visualization

Understanding Geometric Scaling

Geometric scaling is a transformation that enlarges or shrinks a geometric object. It's defined by a scale factor and a center point. Each point of the object is moved away from or towards the center point by a factor proportional to the scale factor.

Formula

If a point P(x, y) is scaled from a center C(cx, cy) by a factor 's', the new point P'(x', y') is calculated as:

x' = cx + (x - cx) * s
y' = cy + (y - cy) * s

How to Use This Tool

1. **Object Coordinates:** Enter the x and y coordinates of the vertices of your geometric object, separated by commas. For example, for a triangle, you might enter '10, 10, 50, 10, 30, 50'. 2. **Scaling Center:** Input the x and y coordinates of the point from which the scaling will be performed. Common centers are (0, 0) for scaling from the origin. 3. **Scale Factor:** Enter a number. A factor greater than 1 will enlarge the object, and a factor between 0 and 1 will shrink it. A factor of 1 will result in no change. 4. Click 'Scale Object' to perform the calculation and visualize the scaled object. 'Reset' will clear all inputs and the visualization.

This tool is helpful for students, educators, and anyone needing to quickly scale geometric shapes for mathematical or design purposes.