Reflection

While a full turn on the xy plane is usually carried out in two dimensions relative to the normal to the plane, the reflection is the same rotation through 180° in three dimensional space and back on the plane about an axis in the plane xy Fig. 1.4 shows examples of two reflections in the plane of the triangle DEF. Reflection about the line y = 0 (axis x) is obtained using the following matrix:

(1.32)

In this case, the new vertices of the triangle D*E*F* will be determined by the transformation

(1.33)

Similarly, the reflection relative to the y -axis (x = 0) has the form

(1.34)

Reflection about the line y = x by using the matrix

(1.35)

Performing transformations, we obtain the vertices coordinates of D**E**F **:

(1.36)

Fig.1.4. Reflection

Reflection about the x -axis has the form:

(1.37)

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