Linear Transformation Calculator (2D) — Rotation, reflection, scaling, and shear
The calculator below will calculate the image of the points in two-dimensional space after applying the transformation.
The above transformations (rotation, reflection, scaling, and shearing) can be represented by matrices. To find the image of a point, we multiply the transformation matrix by a column vector that represents the point's coordinate.
The transformation matrices are as follows:
|Type of transformation||Transformation matrix|
|Clockwise rotation by an angle θ about the origin.
|Counter-clockwise rotation by an angle θ about the origin.
|Reflection against the x-axis.
|Reflection against the y-axis.
|Scaling (contraction or dilation) in all x and y direction by a factor k.
|Horizontal shear (parallel to the x-axis) by a factor m.
|Horizontal shear (parallel to the y-axis) by a factor m.
- Rotate point A (2,3) clockwise about the origin by an angle 90°.
| || = || |
| || |
|cos 90°||sin 90°|
|−sin 90°||cos 90°|| |
| || || |
- Reflect point A (-3,4) against the x-axis