Matrix transformation

Calculates matrix transformation like rotation, reflection, projection, shear (transvection) or stretch.
You may choose exact or numerical solution.

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How to use this calculator ?

This tool calculates,
- the matrix of a geometric transformation like a rotation, an orthogonal projection or a reflection.
- Transformation equations
- The transformation of a given point

Accepted inputs
- numbers and fractions
- usual operators : + - / *
- usual functions : cos, sin , etc
to square root a number, use sqrt e.g. sqrt(3).

Common fields to all transformations

- Transformation field : choose the geometric transformation you want to analyze.
- Calculate transformation of point (x₀,y₀) : this field is not mandatory. If inputed, the tool calculates the transformation of point M (x₀,y₀).
- Solution field : choose to output the exact solution or a solution with numerical values (Exemple : pi vs 3.14159265 ou 3/4 vs 0.75)

Rotation about a point in a plane (2D)

- Angle field : input the angle of the rotation and select the unit (radian or degree) in the select field.
Input a positive valeur. The direction of rotation is determined by the field 'direction' and not by the signe of the angle value.
- Direction field : choose the direction of the rotation (clockwise or counterclockwise).
- Center : input the coordinates of the rotation center separated by a space. If the center of rotation is the origin, input : 0 0

Reflection across a line in a plane (2D)

- Line : m p : if the line equation is y = mx+p, then input m (slope) and p (intercept) separated by a space. Example: for 'y = 2x-4' line, input : 2 -4

Orthogonal projection onto a line of the plane (2D)

- Line : n q field : if the line equation is y = nx+q, then input n (slope) and q (intercept) separated by a space. Example: for 'y = -2x-7' line, input : -2 -7

Scaling (2D)

- factor k : input the factor of the scaling.
This transformation is also called Enlargement when k > 1 and a Contraction when k < 1.

Shear or stretch (2D)

- factor k : input the factor of the transformation. For the direction, a horizontal shear (or transvection) is a shear that is parallel to x-axis.