Transformation Geometry

CONTENT:

(a) Translation of points and shapes on the Cartesian plane.

(b) Reflection of points and shapes on the Cartesian plane.

(c) Rotation of points and shapes on the Cartesian plane.

(d) Enlargement of points and shapes on the Cartesian plane.

Introduction

When the position or dimensions (or both) of a shape changes, we say it is transformed. The image is the figure which results after transformation of the shape. If the image has the same dimension as the original shape, the transformation is called a congruency. (Two shapes are congruent if their corresponding dimensions are congruent).  A transformation is a mapping between two shapes.

Translation of points and shapes on the Cartesian plane.

A Translation is a movement in a straight line. Under a translation every point in a line or plane shape moves the same distance in the same direction by a fixed translation or displacement vector.  Note: \(\begin{pmatrix}x \\ y \end{pmatrix} = (x, y)\)

In general, if the position vector of a point \(\begin{pmatrix}x \\ y \end{pmatrix}\) is given by the translation \(\begin{pmatrix}a \\ b \end{pmatrix}\) the position vector of its image is \(\begin{pmatrix}x + a\\ y + b \end{pmatrix}\).