Composition Of Two Consecutive Translations

Determining a single translation representing the composition of two consecutive translations is the same as determining the resultant two vectors. If the first transactions of T₁ with the column vector (^a1 _b1) are then followed by the second translational T₂ with the column vector (^a2 _b2), the single translation representing the above composition is:

Note:

• The T₁ translation is continued by T₂ translation equal to T₂ translation followed by T₁ translation, ie (T₁ o T₂) = (T₂ o T₁). So the composition of two translations is commutative.
• The map shadow of A(x, y) by T₁ translation is continued by T₁ translation denoted by (T₂ o T₁) A (x, y).

Example:
Translations T₁ and T₂ each have column vectors (² _-3) and (^-5 ₄), find (T₂ o T₁) A (-5, 1)!

Answer:

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Referensi :

• To'Ali's book math group accounting and sales

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