Explore the Geometric Transformations
Drag a shape to translate, rotate and scale it and see the transformation matrix. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Geometric Transformations with sample data entered and the result showing.
What is the Geometric Transformations?
Drag a shape to translate, rotate and scale it and see the transformation matrix. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
Computer graphics, video games, robotics, animation and CAD all use transformations to move and orient objects in 2D and 3D.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
A translation moves a shape without changing its size or orientation.
A rotation turns a shape about a point, and a reflection flips it across a line.
A scale (dilation) multiplies distances from a centre by a factor k.
Drag the shape to translate it by (3, −2).
Rotate by 90° and note the new coordinates.
Scale by 2 and by 0.5.
Used for
Pick one to see how it fits.
Math learners
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
Try it freeTeachers
For teachers: project the Geometric Transformations on the board, let students predict the result, then run it together and test this: Rotate by 90° and note the new coordinates. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
What is a transformation matrix?
A small grid of numbers that turns every point of a shape into its image. Different matrices rotate, scale, reflect or shear.
What is the difference between a reflection and a rotation?
A reflection flips the shape to its mirror image. A rotation turns it about a point but keeps its handedness.
Is the Geometric Transformations free to use?
Yes. The Geometric Transformations is free, needs no signup or download and runs in your web browser. It is part of the Math group of AZRS simulations.
Does the Geometric Transformations work on a phone or tablet?
Yes. The Geometric Transformations takes touch input as well as mouse input, so you can use its 6 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Geometric Transformations?
1. In the Geometric Transformations, use the controls to change Shape, Rotation, Scale factor, Shear along x, Shear along y, and more. The simulation reacts instantly. 2. In the Geometric Transformations, pick an option such as Triangle, Square, House, Arrow to switch modes or load an example. 3. In the Geometric Transformations, press "Reflect in y-axis", "Reflect in x-axis", "Reflect in y = x", "Reflect in y = −x" to start, reset or change what is happening. 4. Start with this experiment: Drag the shape to translate it by (3, −2). Drag any glowing handle, object or slider with your mouse or finger and the Geometric Transformations responds in real time. 5. Change one setting at a time and watch which readout moves, then compare it with this idea: A translation moves a shape without changing its size or orientation.
More free tools
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Try the Geometric Transformations now
Drag a shape to translate, rotate and scale it and see the transformation matrix. Free to use.
Try it free