Understanding Translations
* Translation: A translation is a geometric transformation that moves every point in a plane or space a fixed distance in a specific direction. It doesn't change the shape or size of the object.
Composition of Translations
When you compose two translations, you essentially perform one translation after the other.
* Example: Imagine translating a shape 3 units to the right, and then translating it 2 units up. The overall effect is a single translation of the shape 3 units to the right and 2 units up.
The Result is Still a Translation
The combined effect of two translations is always a single translation. This is because:
* Direction: The resulting translation's direction is determined by the sum of the individual translation vectors.
* Distance: The resulting translation's distance is determined by the sum of the individual translation distances.
Conclusion
Because the composition of two translations results in a shift in a single direction and distance, it is itself a translation.