Reflection

Transformation

A transformation is a general term for four specific ways to manipulate the shape of a point, a line or shape. The original shape of the object is called the final shape and the position of the object is the image under the transformation.

There is three fundamental transformation.

1. Reflection
2. Rotation
3. Translation (or displacement)

Reflection

The reflection of a geometrical figure means the formation of the image of the figure after reflecting about the line of reflection. The line of reflection is also called the axis of reflection.

Properties of reflection

1. The geometrical figure and its image are at equal distance from the axis of reflection.
2. The areas of the geometrical figure and its image are equal.
3. The appearance of the image of a figure is opposite to the figure.

Reflection using coordinates

Very often reflections are performed using coordinates. The coordinates allow us to easily describe the image and its pre-image (object)

Reflection in the x-axis

A reflection in the x-axis can be seen in the picture below. In which A is reflected its image 'A'. The general rule for the reflection in the x-axis:

A ( x, y) → A' (x, -y)

r_x-axis(x, y) = (x, -y)

Reflection in the y-axis

A reflection in the y-axis can be seen in the picture below in which A is reflected its image A'. The general rule for a reflection in the line y=x:

A ( x, y) → A'(y, x) or

r_{y= x} (x, y) = (y, x)

Reflection in the line y = -x

When you reflect a point across the line y = -x, then x- coordinate and y-coordinate change places and are negated. The general rule for the reflection in the line y = -x:

A ( x, y) → A' (-Y, -X) or

r_{y = -x} (x, y) = (-y, -x)

A reflection in the line y = -x can be seen in the picture below in which A is reflected its image A'.