REFLECTION

TRANSLATION

ROTATION

TRANSFORMATION III

TESSELATION PATTERN

Combine transformations

Learning Outcome

• Determine the image of an object under combination of two isometric transformation

Combined Transformation

The combined transformation AB means transformation B followed by transformation A

EXAMPLE:

• The diagram shows triangles I, II, III and IV which are the images of A.

• Given,

T is a translation ,

P is a reflection in the line x = 6, and

R is a rotation through 90º clockwise about the origin

• Determine the image of triangle A under the following combine transformation.

a) TP b) PR c) RT d) TT

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ANSWER

• (a) III

• (b) I

• (c) IV

• (d) II

Notes:

When we combine two isometric transformations, the final image

is exactly the same in size and shape as the object.

ACTIVITY

WORKSHEET 2

• Transformation U represents the translation • Transformation V represents the reflection in the

line x = 2.• Transformation W represents the rotation

through 180º anticlockwise about the origin.

• Determine the image of object Q under the following combine transformation.

(i) VW (ii) UU (iii) UV (iv) WU

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ANSWER

• (i) V

• (ii) III

• (iii) I

• (iv) IV

SUMMARY

- Reflects object at line x or y

If - x positive, move to the right at x –axis and otherwise - y positive, move to the above at y axis and otherwise

- rotate 90º, 180°,270°, and 360°- clockwise or anti-clockwise- respect to origin.

y

x

Combined Two

Isometric Transformation

TranslationReflection Rotation

When we combine two isometric transformations

Final image objectSame in size

THE END!!!