# Matrix transformation

Calculates matrix transformation like rotation, reflection, projection, shear (transvection) or stretch.

You may choose exact or numerical solution.

## 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 (x

_{0},y

_{0}) : this field is not mandatory. If inputed, the tool calculates the transformation of point M (x

_{0},y

_{0}).

- 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.

## See also

Linear algebra Calculators

Coordinate Geometry calculators

Mathematics calculators