Transformations of the Unit Square in the x - y Plane – Level 2 Further Mathematics AQA Revision

Transformations of the Unit Square in the x - y Plane

Understand that transformations can be recognised by the image of the unit square under the transformation.
Scaling is marked by stretching or shrinking of the unit square and is caused by a scalar factor in the matrix.
Rotation is recognised when the unit square is reoriented but maintains the same size and shape.
A reflexion is notable if the image is a mirror version of the unit square.
A shear is typified by the square appearing to be pushed to one side.

Note that the unit square in the x-y plane motivates the concept of any square with sides parallel to the axes.
Be aware that the unit square refers to a square of side length 1, whose bottom-left corner is at the origin.
Remember that transformations can be applied to the unit square to help visualise matrix transformations.

Understand that transformation of the unit square can be represented using matrices to change the position of the points.
Learn to multiply the coordinates of the square by the matrix to find the transformed coordinates. This applies to transformations including enlargement, reflections, rotations and shearing.
Be confident manipulating the unit vectors i (pointing in the direction of one unit on the x-axis) and j (pointing in the direction of one unit on the y-axis).

Understand that an unchanged unit square signifies the identity matrix.
A negative determinant of the transformation matrix indicates a reflexion has occurred.
Keep in mind that the determinant of a transformation matrix gives the area scale factor.
Remember, if the determinant is 1 or -1, the transformation is area-preserving (i.e., the area of the unit square remains the same).