Understanding Coordinate Scale Factors
A coordinate scale factor describes how far a point moves from a fixed center during dilation. It is used in geometry, mapping, graphics, and design checks. When the factor is greater than one, the image grows. When it is between zero and one, the image shrinks. A negative factor places the image on the opposite ray.
Why the Center Matters
This calculator uses the center of dilation and coordinate pairs. It can find the scale factor from original and image points. It can also create image coordinates when the scale is known. The same idea works in two dimensions and three dimensions. Each coordinate is measured from the center first. Then the factor multiplies that measured distance.
Common Coordinate Checks
Coordinate work often fails because the center is ignored. A point may look doubled from the origin, yet not doubled from another center. This tool keeps the center visible. It reports the vector from the center, the distance before dilation, the distance after dilation, and the coordinate ratios. These checks help catch wrong signs and mixed points.
Signed and Absolute Scale
Signed scale is useful when direction matters. A positive value keeps the image on the same ray. A negative value reflects the point through the center. The absolute value shows the size change. Area changes by the square of the factor. Volume changes by the cube of the absolute factor. These extra values help with similarity, models, and spatial scaling.
Accuracy Tips
For best results, enter exact coordinates when possible. Decimal values also work. Use the tolerance field when copied values have rounding noise. A very small tolerance is good for exact homework. A larger tolerance can help with measured map data. Review the consistency note before using the answer in a proof or report.
Batch Coordinate Scaling
The batch box is helpful for polygons. Enter one point per line. The calculator applies the same factor to every point. This creates a scaled shape around the same center. You can copy the table, download a CSV file, or create a PDF report. The result is clear, traceable, and easy to check.
Segment Comparison
The method also supports scale comparisons between segments. Use matching point order. Keep units consistent. Do not mix feet with meters. Small input errors can change a ratio, especially near the chosen dilation center.