Translation
In geometry, translation simply means moving, without rotating, resizing or anything else, just moving. Translation is the term used in geometry to describe a function that moves an object a certain distance.
Summary
In geometry, translation simply means moving, without rotating, resizing or anything else, just moving. Translation is the term used in geometry to describe a function that moves an object a certain distance.
Things to Remember
- Translation is a transformation that "slides" an object at a fixed distance and in a given direction.
- The original object and its translation have the same shape and size, and they face in the same direction.
- An example of translation in architecture would be the stadium setting. The seats are the same size and shape and face in the same direction.
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Translation
In a translation, every point of the object must be moved in the same direction and for the same distance.When you are performing a translation, the initial object is called the pre-image and the object after the translation is called the image. The original object and its translation have the same shape and size, and they face in the same direction. For example, ΔABC is translated by 3 units to the right.
A general rule:
T (x, y)\(\rightarrow\) (x + a, y + b)
In the above graph,
T (-1, 1) \(\rightarrow\) A'(-1 + 3, 1 + 0) = A' (2,1)
T(-2, -1) \(\rightarrow\) B'(-2 + 3, -1 + 0) = B'(1, -1)
T(0, -2) \(\rightarrow\) C' (0 + 3, -2 + 0) = C' (3, -2)
Example
Find the image of the points P (4, 3) under the translation(x, y) → (x+3, y-3).
Solution:
The translation is (x, y) → (x+3, y-3)
The translation tells you to add 3 to the x-value and subtract 3 from the y- value.
So, (4, 3) → (4+3, 3-3) =(7, 0)
Lesson
Transformation
Subject
Compulsory Maths
Grade
Grade 8
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