Transformation Tracker Calculator

Calculator Input

Transformation Type

Input X Coordinate

Input Y Coordinate

Translation X

Translation Y

Rotation Angle (degrees)

Scale Factor X

Scale Factor Y

Shear X Factor

Shear Y Factor

m11

m12

m21

m22

Custom Translate X

Custom Translate Y

Export and Tracker Controls

The tracker stores each submitted transformation during your current session. Export the history as CSV or print-ready PDF.

Tracked Transformation History

Time	Type	Input	Output	Delta	Determinant	Area Scale	Summary
No tracked transformations yet. Submit the form to build your session history.

Example Data Table

Transformation	Input Point	Main Settings	Expected Output	Notes
Translation	(2, 3)	tx = 4, ty = -1	(6, 2)	Add vector values to each coordinate.
Rotation	(1, 0)	90° about origin	(0, 1)	Uses the standard rotation matrix.
Reflection Y-axis	(5, -2)	Axis reflection	(-5, -2)	X changes sign, Y stays constant.
Dilation	(3, 4)	sx = 2, sy = 0.5	(6, 2)	Each axis scales independently.
Shear	(2, 3)	shx = 0.5, shy = 0.2	(3.5, 3.4)	Coordinates lean according to shear factors.
Custom Affine	(1, 2)	[[2,1],[0,1]], t=(3,-1)	(7, 1)	Matrix action plus translation shift.

Formula Used

General affine transformation:

(x′, y′) = A(x, y) + t

Where A is a 2 × 2 matrix and t is a translation vector.

Translation:

x′ = x + t_x

y′ = y + t_y

Rotation about the origin:

x′ = x cos θ − y sin θ

y′ = x sin θ + y cos θ

Dilation:

x′ = s_xx

y′ = s_yy

Shear:

x′ = x + k_xy

y′ = k_yx + y

Determinant meaning:

det(A) = a₁₁a₂₂ − a₁₂a₂₁

The absolute determinant gives the area scale factor.

How to Use This Calculator

Choose a transformation type from the dropdown list.
Enter the original point coordinates.
Fill only the settings related to your chosen transformation.
Click Calculate Transformation to generate the result.
Review the output point, matrix, determinant, and measured changes.
Check the tracker table to compare previous transformations.
Use the CSV button for spreadsheet export.
Use the PDF button to open a print-ready report and save it as PDF from your browser.

FAQs

1. What does this calculator track?

It tracks how a point changes after translation, rotation, reflection, dilation, shear, or a custom affine matrix. It also stores session history, determinant values, coordinate differences, and exportable summaries.

2. Why is the determinant important?

The determinant shows how the matrix changes area. Its absolute value is the area scale factor. A negative determinant also means the transformation reverses orientation.

3. Does translation affect the determinant?

No. Translation shifts the point location, but it does not change the matrix determinant. Determinant comes only from the linear matrix part.

4. Can I use non-integer values?

Yes. The calculator accepts decimal values for coordinates, angles, scale factors, shear factors, and custom matrix entries. This helps with more precise mathematical analysis.

5. What is the difference between dilation and shear?

Dilation stretches or compresses axes directly. Shear slants the shape by mixing one coordinate into the other. They produce very different geometric effects.

6. Does this tool support repeated steps?

It tracks multiple submitted transformations in session history. You can compare entries over time, but each calculation applies to the entered point independently.

7. How does the PDF option work?

The PDF button opens a print-friendly report. Your browser print dialog appears automatically, and you can choose Save as PDF to create the file.

8. Is this useful for classroom work?

Yes. It is useful for geometry practice, matrix lessons, coordinate analysis, quick demonstrations, and comparing how different transformations affect the same point.